@article {MR1317641,
    AUTHOR = {Coleman, Robert F. and Gouv{\^e}a, Fernando Q. and Jochnowitz,
              Naomi},
     TITLE = {{$E\sb 2$}, {$\Theta$}, and overconvergence},
   JOURNAL = {Internat. Math. Res. Notices},
  FJOURNAL = {International Mathematics Research Notices},
      YEAR = {1995},
    NUMBER = {1},
     PAGES = {23--41 (electronic)},
      ISSN = {1073-7928},
   MRCLASS = {11F33 (11F85)},
  MRNUMBER = {MR1317641 (96d:11047)},
MRREVIEWER = {Andrea Mori},
}

@article {MR1977007,
    AUTHOR = {Greenberg, Ralph},
     TITLE = {Galois theory for the {S}elmer group of an abelian variety},
   JOURNAL = {Compositio Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {136},
      YEAR = {2003},
    NUMBER = {3},
     PAGES = {255--297},
      ISSN = {0010-437X},
     CODEN = {CMPMAF},
   MRCLASS = {11G10 (11G05 11R23 11R34)},
  MRNUMBER = {MR1977007 (2004c:11097)},
MRREVIEWER = {Vinayak Vatsal},
}


@article {MR1740990,
    AUTHOR = {Wan, Daqing},
     TITLE = {Dwork's conjecture on unit root zeta functions},
   JOURNAL = {Ann. of Math. (2)},
  FJOURNAL = {Annals of Mathematics. Second Series},
    VOLUME = {150},
      YEAR = {1999},
    NUMBER = {3},
     PAGES = {867--927},
      ISSN = {0003-486X},
     CODEN = {ANMAAH},
   MRCLASS = {11G40 (11G25 14F30 14G10 14G15)},
  MRNUMBER = {MR1740990 (2001a:11108)},
MRREVIEWER = {Yuichiro Taguchi},
}


@article {MR2122612,
    AUTHOR = {Joyce, Adam},
     TITLE = {The {M}anin constant of an optimal quotient of {$J\sb
              0(431)$}},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {110},
      YEAR = {2005},
    NUMBER = {2},
     PAGES = {325--330},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {11G10 (11F33 11G18)},
  MRNUMBER = {MR2122612},
MRREVIEWER = {Mihran Papikian},
}

@incollection {MR2088713,
    AUTHOR = {Flach, Matthias},
     TITLE = {The equivariant {T}amagawa number conjecture: a survey},
 BOOKTITLE = {Stark's conjectures: recent work and new directions},
    SERIES = {Contemp. Math.},
    VOLUME = {358},
     PAGES = {79--125},
      NOTE = {With an appendix by C.\ Greither},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2004},
   MRCLASS = {11G40 (11G18 11R23 11R33)},
  MRNUMBER = {MR2088713},
MRREVIEWER = {Nigel Byott},
}


@book {MR2090725,
     TITLE = {Stark's conjectures: recent work and new directions},
    SERIES = {Contemporary Mathematics},
    VOLUME = {358},
    EDITOR = {Burns, David and Sands, Jonathan},
      NOTE = {Papers from the International Conference on Stark's
              Conjectures and Related Topics held at Johns Hopkins
              University, Baltimore, MD, August 5--9, 2002},
 PUBLISHER = {American Mathematical Society},
   ADDRESS = {Providence, RI},
      YEAR = {2004},
     PAGES = {x+221},
      ISBN = {0-8218-3480-0},
   MRCLASS = {11-06 (11R42)},
  MRNUMBER = {MR2090725 (2005d:11004)},
}


@article {MR2135139,
    AUTHOR = {Vatsal, V.},
     TITLE = {Multiplicative subgroups of {$J\sb 0(N)$} and applications to
              elliptic curves},
   JOURNAL = {J. Inst. Math. Jussieu},
  FJOURNAL = {Journal of the Institute of Mathematics of Jussieu. JIMJ.
              Journal de l'Institute de Math\'ematiques de Jussieu},
    VOLUME = {4},
      YEAR = {2005},
    NUMBER = {2},
     PAGES = {281--316},
      ISSN = {1474-7480},
   MRCLASS = {11G05 (11G18)},
  MRNUMBER = {MR2135139},
}

@article{bluher:formal,
   author={Bluher, Antonia W.},
   title = {A {L}eisurely {I}ntroduction to {F}ormal {G}roups
and {E}lliptic {C}urves,\\
   {\tt http://www.math.uiuc.edu/Algebraic-Number-Theory/0076/}}
}



@incollection {MR1263527,
    AUTHOR = {Nekov{\'a}{\v{r}}, Jan},
     TITLE = {On {$p$}-adic height pairings},
 BOOKTITLE = {S\'eminaire de Th\'eorie des Nombres, Paris, 1990--91},
    SERIES = {Progr. Math.},
    VOLUME = {108},
     PAGES = {127--202},
 PUBLISHER = {Birkh\"auser Boston},
   ADDRESS = {Boston, MA},
      YEAR = {1993},
   MRCLASS = {11G09 (11F85 14F30)},
  MRNUMBER = {MR1263527 (95j:11050)},
MRREVIEWER = {Abdellah Mokrane},
}


 
@book {MR1263519,
     TITLE = {S\'eminaire de {T}h\'eorie des {N}ombres, {P}aris, 1990--91},
    SERIES = {Progress in Mathematics},
    VOLUME = {108},
    EDITOR = {David, Sinnou},
      NOTE = {Papers from the seminar held in Paris, 1990--1991},
 PUBLISHER = {Birkh\"auser Boston Inc.},
   ADDRESS = {Boston, MA},
      YEAR = {1993},
     PAGES = {vi+282},
      ISBN = {0-8176-3684-6},
   MRCLASS = {11-06},
  MRNUMBER = {MR1263519 (94i:11005)},
}

@incollection {MR1042777,
    AUTHOR = {Zarhin, Yuri G.},
     TITLE = {{$p$}-adic heights on abelian varieties},
 BOOKTITLE = {S\'eminaire de Th\'eorie des Nombres, Paris 1987--88},
    SERIES = {Progr. Math.},
    VOLUME = {81},
     PAGES = {317--341},
 PUBLISHER = {Birkh\"auser Boston},
   ADDRESS = {Boston, MA},
      YEAR = {1990},
   MRCLASS = {11G10 (14K15)},
  MRNUMBER = {MR1042777 (91f:11043)},
MRREVIEWER = {Michel Gros},
}

 
@book {MR1042761,
     TITLE = {S\'eminaire de {T}h\'eorie des {N}ombres, {P}aris 1987--88},
    SERIES = {Progress in Mathematics},
    VOLUME = {81},
    EDITOR = {Goldstein, Catherine},
      NOTE = {Papers from the seminar held in Paris, 1987--88},
 PUBLISHER = {Birkh\"auser Boston Inc.},
   ADDRESS = {Boston, MA},
      YEAR = {1990},
     PAGES = {viii+350},
      ISBN = {0-8176-3458-4},
   MRCLASS = {11-06},
  MRNUMBER = {MR1042761 (90j:11004)},
}


@incollection {MR1299736,
    AUTHOR = {Plater, Andrew},
     TITLE = {Supersingular {$p$}-adic height pairings on elliptic curves},
 BOOKTITLE = {Arithmetic geometry (Tempe, AZ, 1993)},
    SERIES = {Contemp. Math.},
    VOLUME = {174},
     PAGES = {95--105},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {1994},
   MRCLASS = {11G07 (11G05)},
  MRNUMBER = {MR1299736 (95h:11056)},
MRREVIEWER = {Jan Nekov{\'a}{\v{r}}},
}

 
@book {MR1299731,
     TITLE = {Arithmetic geometry},
    SERIES = {Contemporary Mathematics},
    VOLUME = {174},
    EDITOR = {Childress, Nancy and Jones, John W.},
      NOTE = {Papers from the Conference on Arithmetic Geometry with an
              Emphasis on Iwasawa Theory held at Arizona State University,
              Tempe, Arizona, March 15--18, 1993},
 PUBLISHER = {American Mathematical Society},
   ADDRESS = {Providence, RI},
      YEAR = {1994},
     PAGES = {x+220},
      ISBN = {0-8218-5174-8},
   MRCLASS = {11-06 (11Fxx 11Gxx)},
  MRNUMBER = {MR1299731 (95d:11002)},
}


@article {MR1091621,
    AUTHOR = {Coleman, Robert F.},
     TITLE = {The universal vectorial bi-extension and {$p$}-adic heights},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {103},
      YEAR = {1991},
    NUMBER = {3},
     PAGES = {631--650},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {14F30 (14K15)},
  MRNUMBER = {MR1091621 (92k:14021)},
MRREVIEWER = {Gerd Faltings},
}


@article {MR2021039,
    AUTHOR = {Iovita, Adrian and Werner, Annette},
     TITLE = {{$p$}-adic height pairings on abelian varieties with
              semistable ordinary reduction},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
    VOLUME = {564},
      YEAR = {2003},
     PAGES = {181--203},
      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {11G50 (11G10 14F40 14K15)},
  MRNUMBER = {MR2021039 (2004j:11066)},
MRREVIEWER = {Alessandra Bertapelle},
}

@incollection {MR2076563,
    AUTHOR = {Besser, Amnon},
     TITLE = {The {$p$}-adic height pairings of {C}oleman-{G}ross and of
              {N}ekov\'a\v r},
 BOOKTITLE = {Number theory},
    SERIES = {CRM Proc. Lecture Notes},
    VOLUME = {36},
     PAGES = {13--25},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2004},
   MRCLASS = {11G50 (11G25 11G30)},
  MRNUMBER = {MR2076563 (2005f:11130)},
MRREVIEWER = {Mark Kisin},
}

 
@book {MR2070918,
     TITLE = {Number theory},
    SERIES = {CRM Proceedings \& Lecture Notes},
    VOLUME = {36},
    EDITOR = {Kisilevsky, Hershy and Goren, Eyal Z.},
      NOTE = {Papers from the 7th Conference of the Canadian Number Theory
              Association held at the University of Montreal, Montreal, QC,
              May 19--25, 2002},
 PUBLISHER = {American Mathematical Society},
   ADDRESS = {Providence, RI},
      YEAR = {2004},
     PAGES = {xiv+303},
      ISBN = {0-8218-3331-6},
   MRCLASS = {11-06},
  MRNUMBER = {MR2070918 (2005b:11004)},
}

@article {perrin-riou:expmath,
    AUTHOR = {Perrin-Riou, Bernadette},
     TITLE = {Arithm\'etique des courbes elliptiques \`a r\'eduction
              supersinguli\`ere en {$p$}},
   JOURNAL = {Experiment. Math.},
  FJOURNAL = {Experimental Mathematics},
    VOLUME = {12},
      YEAR = {2003},
    NUMBER = {2},
     PAGES = {155--186},
      ISSN = {1058-6458},
   MRCLASS = {11G40 (11G05 11R23)},
  MRNUMBER = {MR2016704 (2005h:11138)},
}

@article {mazur-tate:refined,
    AUTHOR = {Mazur, B. and Tate, J.},
     TITLE = {Refined conjectures of the ``{B}irch and {S}winnerton-{D}yer
              type''},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {54},
      YEAR = {1987},
    NUMBER = {2},
     PAGES = {711--750},
      ISSN = {0012-7094},
     CODEN = {DUMJAO},
   MRCLASS = {11G40 (11G05 14G25 14K15)},
  MRNUMBER = {MR899413 (88k:11039)},
MRREVIEWER = {Karl Rubin},
}

@article {wuthrich:heightfamily,
    AUTHOR = {Wuthrich, Christian},
     TITLE = {On {$p$}-adic heights in families of elliptic curves},
   JOURNAL = {J. London Math. Soc. (2)},
  FJOURNAL = {Journal of the London Mathematical Society. Second Series},
    VOLUME = {70},
      YEAR = {2004},
    NUMBER = {1},
     PAGES = {23--40},
      ISSN = {0024-6107},
     CODEN = {JLMSAK},
   MRCLASS = {11G50 (11G05)},
  MRNUMBER = {MR2064750},
}

@article {schneider:height1,
    AUTHOR = {Schneider, Peter},
     TITLE = {{$p$}-adic height pairings. {I}},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {69},
      YEAR = {1982},
    NUMBER = {3},
     PAGES = {401--409},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {14K15 (12A70 14G25)},
  MRNUMBER = {MR679765 (84e:14034)},
MRREVIEWER = {Reinhard B{\"o}lling},
}

@article {schneider:height2,
    AUTHOR = {Schneider, Peter},
     TITLE = {{$p$}-adic height pairings. {II}},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {79},
      YEAR = {1985},
    NUMBER = {2},
     PAGES = {329--374},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {11G10 (11G40 11R23 14G25)},
  MRNUMBER = {MR778132 (86j:11063)},
MRREVIEWER = {Reinhard B{\"o}lling},
}


@incollection {mazur-tate:canonical,
    AUTHOR = {Mazur, B. and Tate, J.},
     TITLE = {Canonical height pairings via biextensions},
 BOOKTITLE = {Arithmetic and geometry, Vol. I},
    SERIES = {Progr. Math.},
    VOLUME = {35},
     PAGES = {195--237},
 PUBLISHER = {Birkh\"auser Boston},
   ADDRESS = {Boston, MA},
      YEAR = {1983},
   MRCLASS = {14K15 (11G10 11G35 14G25)},
  MRNUMBER = {MR717595 (85j:14081)},
MRREVIEWER = {Yu. G. Zarkhin},
}
@book {MR717602,
     TITLE = {Arithmetic and geometry. {V}ol. {II}},
    SERIES = {Progress in Mathematics},
    VOLUME = {36},
    EDITOR = {Artin, Michael and Tate, John},
      NOTE = {Geometry,
              Papers dedicated to I. R. Shafarevich on the occasion of his
              sixtieth birthday},
 PUBLISHER = {Birkh\"auser Boston},
   ADDRESS = {Mass.},
      YEAR = {1983},
     PAGES = {vi+481},
      ISBN = {3-7643-3133-X},
   MRCLASS = {14-06},
  MRNUMBER = {MR717602 (84j:14005b)},
}
@book {MR717586,
     TITLE = {Arithmetic and geometry. {V}ol. {I}},
    SERIES = {Progress in Mathematics},
    VOLUME = {35},
    EDITOR = {Artin, Michael and Tate, John},
      NOTE = {Arithmetic,
              Papers dedicated to I. R. Shafarevich on the occasion of his
              sixtieth birthday},
 PUBLISHER = {Birkh\"auser Boston},
   ADDRESS = {Mass.},
      YEAR = {1983},
     PAGES = {vi+359},
      ISBN = {3-7643-3132-1},
   MRCLASS = {14-06 (10-06 12-06)},
  MRNUMBER = {MR717586 (84j:14005a)},
}


@incollection {katz:padicprop,
    AUTHOR = {Katz, Nicholas M.},
     TITLE = {{$p$}-adic properties of modular schemes and modular forms},
 BOOKTITLE = {Modular functions of one variable, III (Proc. Internat. Summer
              School, Univ. Antwerp, Antwerp, 1972)},
     PAGES = {69--190. Lecture Notes in Mathematics, Vol. 350},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1973},
   MRCLASS = {10D15 (14D20)},
  MRNUMBER = {MR0447119 (56 \#5434)},
MRREVIEWER = {V. V. Sokurov},
}

@book {MR0323724,
     TITLE = {Modular functions of one variable. {III}},
 BOOKTITLE = {Proceedings of the International Summer School, University of
              Antwerp, RUCA, July 17--August 3, 1972},
    EDITOR = {Kuyk, Willem and Serre, J.-P.},
      NOTE = {Lecture Notes in Mathematics, Vol. 350},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1973},
     PAGES = {iv+350},
   MRCLASS = {10D05 (14K22)},
  MRNUMBER = {MR0323724 (48 \#2080)},
}

@article {malle:distro,
    AUTHOR = {Malle, G.},
     TITLE = {On the distribution of {G}alois groups},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {92},
      YEAR = {2002},
    NUMBER = {2},
     PAGES = {315--329},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {12F12 (11R32 11R47 12F10)},
  MRNUMBER = {MR1884706 (2002k:12010)},
MRREVIEWER = {Helmut V{\"o}lklein},
}


 
@article {malle:distro2,
    AUTHOR = {Malle, G.},
     TITLE = {On the distribution of {G}alois groups. {II}},
   JOURNAL = {Experiment. Math.},
  FJOURNAL = {Experimental Mathematics},
    VOLUME = {13},
      YEAR = {2004},
    NUMBER = {2},
     PAGES = {129--135},
      ISSN = {1058-6458},
   MRCLASS = {11R32 (11R47 12F10)},
  MRNUMBER = {MR2068887 (2005g:11216)},
MRREVIEWER = {F. Diaz y Diaz},
}

@incollection {cohen-diaz-olivier:disc,
    AUTHOR = {Cohen, Henri and Diaz y Diaz, Francisco and Olivier, Michel},
     TITLE = {Counting discriminants of number fields of degree up to four},
 BOOKTITLE = {Algorithmic number theory (Leiden, 2000)},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {1838},
     PAGES = {269--283},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2000},
   MRCLASS = {11R29 (11R21 11Y40)},
  MRNUMBER = {MR1850611 (2002g:11148)},
MRREVIEWER = {Joe P. Buhler},
}




@article {delaunay:heuristics,
    AUTHOR = {Delaunay, Christophe},
     TITLE = {Heuristics on {T}ate-{S}hafarevitch groups of elliptic curves
              defined over {$\Bbb Q$}},
   JOURNAL = {Experiment. Math.},
  FJOURNAL = {Experimental Mathematics},
    VOLUME = {10},
      YEAR = {2001},
    NUMBER = {2},
     PAGES = {191--196},
      ISSN = {1058-6458},
   MRCLASS = {11G05 (11R29 11R45)},
  MRNUMBER = {MR1837670 (2003a:11065)},
MRREVIEWER = {M. Ram Murty},
}

@proceedings {MR1850596,
     TITLE = {Algorithmic number theory},
    SERIES = {Lecture Notes in Computer Science},
    VOLUME = {1838},
 BOOKTITLE = {Proceedings of the 4th International Symposium (ANTS-IV) held
              at the Universiteit Leiden, Leiden, July 2--7, 2000},
    EDITOR = {Bosma, Wieb},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {2000},
     PAGES = {x+613},
      ISBN = {3-540-67695-3},
   MRCLASS = {11-06 (11Yxx)},
  MRNUMBER = {MR1850596 (2002d:11002)},
}


@incollection {elkies:ants4,
    AUTHOR = {Elkies, N.\thinspace{}D.},
     TITLE = {Rational points near curves and small nonzero {$\vert x\sp
              3-y\sp 2\vert $} via lattice reduction},
 BOOKTITLE = {Algorithmic number theory (Leiden, 2000)},
    SERIES = {Lecture Notes in Comput. Sci.},
    VOLUME = {1838},
     PAGES = {33--63},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {2000},
MRREVIEWER = {R. C. Baker},
}


@article{rank4,
   author={Jorza, A. and Balakrishna, J. and Stein, W.},
   title = {The {S}mallest {C}onductor for an {E}lliptic {C}urve of {R}ank 
  {F}our is {C}omposite},
   year = {2003},
   journal={{\tt http://modular.fas.harvard.edu/rank4/}}

}

@article{cremona-watkins:lattice-distro,
   author={Cremona, J. and Watkins, M.},
   title={Lattice {D}istribution of {M}ordell-{W}eil {G}roups of {E}lliptic {C}urves},
   journal={In Preparation}
}


@article{watkins:cubic,
   author={Watkins, M.},
   title={Rank distribution in a family of cubic twists},
   year={2004},
   journal={{\tt http://www.arxiv.org/abs/math.NT/0412427}}
}

@article{connell:echb,
   author = {Connell, I.},
   title = {The {E}lliptic {C}urves {H}andbook,\\
{\tt http://www.math.mcgill.ca/connell/public/ECH1/}},
   year = {2005}
}

@article{bhargava:density,
   author = {Bhargava, M.},
   title = {The density of discriminants of quartic rings and fields},
   VOLUME = {162},
   number = {2},
   year = {2005},
   journal = {Annals of Mathematics}
}

@article{bsdalg1,
    author={G.~Grigorov and A.~Jorza and S.~Patrikis and C.~Patrascu and W.~Stein},
    title={Verification of the {B}irch and {S}winnerton-{D}yer {C}onjecture for
  {S}pecific {E}lliptic {C}urves},
    year = {2005},
    journal = {(Submitted)\\{\tt http://modular.fas.harvard.edu/papers/bsdalg/}}
}


@article{matplotlib,
   author = {John Hunter},
   title = {matplotlib: {P}ython software for drawing graphs},
   year = {2005},
   journal = {{\tt http://matplotlib.sourceforge.net/}}
}

@incollection {zhang:gzgl2,
    AUTHOR = {Zhang, Shou-Wu},
     TITLE = {Gross-{Z}agier formula for {$\rm GL(2)$}. {II}},
 BOOKTITLE = {Heegner points and Rankin $L$-series},
    SERIES = {Math. Sci. Res. Inst. Publ.},
    VOLUME = {49},
     PAGES = {191--214},
 PUBLISHER = {Cambridge Univ. Press},
   ADDRESS = {Cambridge},
      YEAR = {2004},
   MRCLASS = {11G40 (11F66)},
  MRNUMBER = {MR2083213},
}



@article{stoll:3descent,
   author = {Stoll, M.},
   title = {Explicit $3$-Descent in {M}agma\\
{\tt http://www.faculty.iu-bremen.de/stoll/magma/explicit-3descent/}},
   year = {2005}
}

@article{prickett:phd,
   author = {Prickett, M.},
   title = {Saturation of {M}ordell-{W}eil {G}roups of {E}lliptic {C}urves over
{N}umber {F}ields},
   year = {2004},
   journal = {U. Nottingham, Ph.D. thesis\\
{\tt http://etheses.nottingham.ac.uk/archive/00000052/}}
}
  

@article{pacetti-villegas-p2,
   author = {Pacetti, A. and Rodriguez-Villegas, F.},
   title = {Computing {W}eight 2 {M}odular {F}orms of {L}evel $p^2$},
   year = {2004},
   volume = {74},
   number = {251},
   pages = {1545--1557},
   journal = {Math. Comp.}
}

@article{dembele:hilbertmod5,
   author = {Demb\'el\'e, L.},
   title = {Explicit {C}omputation of {H}ilbert {M}odular {F}orms 
on {$\Q(\sqrt{5})$}},
   year = {2005}
}

@article{grigor:phd,
   author = {Grigorov, G.},
   title = {{K}ato's {E}uler {S}ystem and the {M}ain {C}onjecture},
   journal = {Harvard {P}h.{D}. {T}hesis},
   year = {2005}
}

@article {ono-skinner:nonvanish,
    AUTHOR = {Ono, Ken and Skinner, Christopher},
     TITLE = {Non-vanishing of quadratic twists of modular {$L$}-functions},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {134},
      YEAR = {1998},
    NUMBER = {3},
     PAGES = {651--660},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {11F67 (11G40)},
  MRNUMBER = {MR1660945 (2000a:11077)},
MRREVIEWER = {A. Perelli},
}


@article {ono:nonvanish_twist,
    AUTHOR = {Ono, Ken},
     TITLE = {Nonvanishing of quadratic twists of modular {$L$}-functions
              and applications to elliptic curves},
   JOURNAL = {J. Reine Angew. Math.},
  FJOURNAL = {Journal f\"ur die Reine und Angewandte Mathematik},
    VOLUME = {533},
      YEAR = {2001},
     PAGES = {81--97},
      ISSN = {0075-4102},
     CODEN = {JRMAA8},
   MRCLASS = {11F67 (11G05 11G40)},
  MRNUMBER = {MR1823865 (2002a:11051)},
MRREVIEWER = {Vinayak Vatsal},
}


@article {waldspurger:valeurs,
    AUTHOR = {Waldspurger, J.-L.},
     TITLE = {Sur les valeurs de certaines fonctions {$L$} automorphes en
              leur centre de sym\'etrie},
   JOURNAL = {Compositio Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {54},
      YEAR = {1985},
    NUMBER = {2},
     PAGES = {173--242},
      ISSN = {0010-437X},
     CODEN = {CMPMAF},
   MRCLASS = {11F70 (11F67 22E55)},
  MRNUMBER = {MR783511 (87g:11061b)},
MRREVIEWER = {Stephen Gelbart},
}
@article {waldspurger:gl2,
    AUTHOR = {Waldspurger, J.-L.},
     TITLE = {Quelques propri\'et\'es arithm\'etiques de certaines formes
              automorphes sur {${\rm GL}(2)$}},
   JOURNAL = {Compositio Math.},
  FJOURNAL = {Compositio Mathematica},
    VOLUME = {54},
      YEAR = {1985},
    NUMBER = {2},
     PAGES = {121--171},
      ISSN = {0010-437X},
     CODEN = {CMPMAF},
   MRCLASS = {11F70 (22E55)},
  MRNUMBER = {MR783510 (87g:11061a)},
MRREVIEWER = {Stephen Gelbart},
}


@article {gonzalez:bsd,
    AUTHOR = {Gonzalez-Avil{\'e}s, Cristian D.},
     TITLE = {On the conjecture of {B}irch and {S}winnerton-{D}yer},
   JOURNAL = {Trans. Amer. Math. Soc.},
  FJOURNAL = {Transactions of the American Mathematical Society},
    VOLUME = {349},
      YEAR = {1997},
    NUMBER = {10},
     PAGES = {4181--4200},
      ISSN = {0002-9947},
     CODEN = {TAMTAM},
   MRCLASS = {11G40 (11G05)},
  MRNUMBER = {MR1390036 (98c:11062)},
MRREVIEWER = {Eric Liverance},
}

@article {mazur-rubin:kolyvagin_systems,
    AUTHOR = {Mazur, Barry and Rubin, Karl},
     TITLE = {Kolyvagin systems},
   JOURNAL = {Mem. Amer. Math. Soc.},
  FJOURNAL = {Memoirs of the American Mathematical Society},
    VOLUME = {168},
      YEAR = {2004},
    NUMBER = {799},
     PAGES = {viii+96},
      ISSN = {0065-9266},
     CODEN = {MAMCAU},
   MRCLASS = {11R34 (11F80 11G40 11R23)},
  MRNUMBER = {MR2031496 (2005b:11179)},
MRREVIEWER = {Thomas A. Weston},
}

@article {matsuno:finitelambda,
    AUTHOR = {Matsuno, Kazuo},
     TITLE = {Finite {$\Lambda$}-submodules of {S}elmer groups of abelian
              varieties over cyclotomic {$\mathbb Z\sb p$}-extensions},
   JOURNAL = {J. Number Theory},
  FJOURNAL = {Journal of Number Theory},
    VOLUME = {99},
      YEAR = {2003},
    NUMBER = {2},
     PAGES = {415--443},
      ISSN = {0022-314X},
     CODEN = {JNUTA9},
   MRCLASS = {11G10},
  MRNUMBER = {MR1969183 (2004c:11098)},
MRREVIEWER = {Ivica Gusi{\'c}},
}

@article{sage,
  author = {Stein, William and Joyner, David},
  title	 = {SAGE: System for Algebra and Geometry Experimentation},
  journal= {Communications in Computer Algebra (SIGSAM Bulletin)},
  year   = {July 2005},
  note   = {{\tt http://sage.sourceforge.net/}.}
}

@article{jorza:seniorthesis,
   AUTHOR = {Jorza, A.},
   TITLE = {The {B}irch and {S}winnerton-{D}yer {C}onjecture for {A}belian 
   {V}arieties over {N}umber {F}ields},
   journal = {Harvard University Senior Thesis},
    year= {2005}
}

@article{ribet:congrel,
    AUTHOR = {Ribet, Kenneth A.},
     TITLE = {Congruence relations between modular forms},
 JOURNAL = {Proc. International Congress of Mathematicians},
     PAGES = {503--514},
      YEAR = {1983}
}

}

@book {darmon:ratpoints,
    AUTHOR = {Darmon, Henri},
     TITLE = {Rational points on modular elliptic curves},
    SERIES = {CBMS Regional Conference Series in Mathematics},
    VOLUME = {101},
 PUBLISHER = {Published for the Conference Board of the Mathematical
              Sciences, Washington, DC},
      YEAR = {2004},
     PAGES = {xii+129},
      ISBN = {0-8218-2868-1},
   MRCLASS = {11G40 (11F67 11F85 11G05 11G18)},
  MRNUMBER = {MR2020572 (2004k:11103)},
MRREVIEWER = {Chandrashekhar Khare},
}

@article {kedlaya:counting_mw,
    AUTHOR = {Kedlaya, Kiran S.},
     TITLE = {Counting points on hyperelliptic curves using
              {M}onsky-{W}ashnitzer cohomology},
   JOURNAL = {J. Ramanujan Math. Soc.},
  FJOURNAL = {Journal of the Ramanujan Mathematical Society},
    VOLUME = {16},
      YEAR = {2001},
    NUMBER = {4},
     PAGES = {323--338},
      ISSN = {0970-1249},
   MRCLASS = {14G05 (11G25 14F43 14G15)},
  MRNUMBER = {MR1877805 (2002m:14019)},
MRREVIEWER = {Miriam D. Abd{\'o}n},
}


@article {katz:padic_interp,
    AUTHOR = {Katz, Nicholas M.},
     TITLE = {{$p$}-adic interpolation of real analytic {E}isenstein series},
   JOURNAL = {Ann. of Math. (2)},
    VOLUME = {104},
      YEAR = {1976},
    NUMBER = {3},
     PAGES = {459--571},
   MRCLASS = {14G10 (10D25)},
  MRNUMBER = {MR0506271 (58 \#22071)},
MRREVIEWER = {V. V. Sokurov},
}

@article{cojocaru-kani:surj,
       AUTHOR = {Cojocaru, Alina Carmen and Kani, Ernst},
   TITLE = {On the surjectivity of the Galois representations associated to
non-CM elliptic curves}
}

@article {cojocaru-kani,
    AUTHOR = {Cojocaru, Alina Carmen and Kani, Ernst},
     TITLE = {The modular degree and the congruence number of a weight 2
              cusp form},
   JOURNAL = {Acta Arith.},
  FJOURNAL = {Acta Arithmetica},
    VOLUME = {114},
      YEAR = {2004},
    NUMBER = {2},
     PAGES = {159--167},
      ISSN = {0065-1036},
     CODEN = {AARIA9},
   MRCLASS = {11F33 (11F11 11G18)},
  MRNUMBER = {MR2068855},
MRREVIEWER = {Siman Wong},
}


@article {stein-watkins:ns,
    AUTHOR = {Stein, W. and Watkins, M.},
     TITLE = {Modular parametrizations of {N}eumann-{S}etzer elliptic
              curves},
   JOURNAL = {Int. Math. Res. Not.},
  FJOURNAL = {International Mathematics Research Notices},
      YEAR = {2004},
    NUMBER = {27},
     PAGES = {1395--1405},
      ISSN = {1073-7928},
   MRCLASS = {11G05 (11G18)},
  MRNUMBER = {MR2052021 (2005c:11070)},
MRREVIEWER = {Siman Wong},
}


@incollection {cohen-lenstra:heuristics,
    AUTHOR = {Cohen, H. and Lenstra, Jr., H. W.},
     TITLE = {Heuristics on class groups of number fields},
 BOOKTITLE = {Number theory, Noordwijkerhout 1983 (Noordwijkerhout, 1983)},
    SERIES = {Lecture Notes in Math.},
    VOLUME = {1068},
     PAGES = {33--62},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1984},
   MRCLASS = {11R29 (13C13)},
  MRNUMBER = {MR756082 (85j:11144)},
MRREVIEWER = {F. J. van der Linden},
}

@proceedings {MR756078,
     TITLE = {Number theory, {N}oordwijkerhout 1983},
    SERIES = {Lecture Notes in Mathematics},
    VOLUME = {1068},
 BOOKTITLE = {Proceedings of the thirteenth Journ\'ees Arithm\'etiques held
              at Noordwijkerhout, July 11--15, 1983},
    EDITOR = {Jager, H.},
 PUBLISHER = {Springer-Verlag},
   ADDRESS = {Berlin},
      YEAR = {1984},
     PAGES = {v+296},
      ISBN = {3-540-13356-9},
   MRCLASS = {11-06},
  MRNUMBER = {MR756078 (85i:11001)},
}

@article {zhang:gz_formulas,
    AUTHOR = {Zhang, Shou-Wu},
     TITLE = {Gross-{Z}agier formula for {${\rm GL}\sb 2$}},
   JOURNAL = {Asian J. Math.},
  FJOURNAL = {The Asian Journal of Mathematics},
    VOLUME = {5},
      YEAR = {2001},
    NUMBER = {2},
     PAGES = {183--290},
      ISSN = {1093-6106},
   MRCLASS = {11G18 (11F67 11G50 14G35)},
  MRNUMBER = {MR1868935 (2003k:11101)},
MRREVIEWER = {Douglas L. Ulmer}
}

@article {buchmann_lenstra:approx,
    AUTHOR = {Buchmann, J. A. and Lenstra, Jr., H. W.},
     TITLE = {Approximating rings of integers in number fields},
   JOURNAL = {J. Th\'eor. Nombres Bordeaux},
  FJOURNAL = {Journal de Th\'eorie des Nombres de Bordeaux},
    VOLUME = {6},
      YEAR = {1994},
    NUMBER = {2},
     PAGES = {221--260},
      ISSN = {1246-7405},
   MRCLASS = {11R04 (11Y40)},
  MRNUMBER = {MR1360644 (96m:11092)},
MRREVIEWER = {Joe P. Buhler}
}

@article{zagier:primes50,
   author = {Zagier, D.},
   title = {The First 50 Million Prime Numbers},
   year = {1975},
   note = {{\tt http://modular.fas.harvard.edu/scans/papers/zagier/}}
}

@book{stein:ent,
   author = {Stein, W.\thinspace{}A.},
   title = {Elementary {N}umber {T}heory,\\
{\tt http://modular.fas.harvard.edu/ent/}},
   year = {2005}
}

@article{rsa, 
   author = {RSA Security Solutions}, 
   title = {{\tt http://www.rsasecurity.com/}}
}

@article{mazur-rubin:large_selmer,
   author = {Rubin, K. and Mazur, B.},
   title = {Finding Large Selmer Groups},
   year = {2005},
   note = {in preparation}
}

@article{jetchev-stein:higher,
   author = {Jetchev, D. and Stein, W.},
    title = {Visibility of {S}hafarevich-{T}ate {G}roups at {H}igher {L}evel},
    year = {2005},
    note = {in preparation}
}

@article {mazur-ribet,
    AUTHOR = {Mazur, B. and Ribet, K. A.},
     TITLE = {Two-dimensional representations in the arithmetic of modular
              curves},
      NOTE = {Courbes modulaires et courbes de Shimura (Orsay, 1987/1988)},
   JOURNAL = {Ast\'erisque},
  FJOURNAL = {Ast\'erisque},
    NUMBER = {196-197},
      YEAR = {1991},
     PAGES = {6, 215--255 (1992)},
      ISSN = {0303-1179},
   MRCLASS = {11F80 (11F25 11G18)},
  MRNUMBER = {MR1141460 (93d:11056)},
MRREVIEWER = {Jacques Tilouine},
}

 
@incollection {ribet:comp,
    AUTHOR = {Ribet, Kenneth A.},
     TITLE = {On the component groups and the {S}himura subgroup of {$J\sb
              0(N)$}},
 BOOKTITLE = {S\'eminaire de Th\'eorie des Nombres, 1987--1988 (Talence,
              1987--1988)},
     PAGES = {Exp.\ No.\ 6, 10},
 PUBLISHER = {Univ. Bordeaux I},
   ADDRESS = {Talence},
      YEAR = {19??},
   MRCLASS = {11G05 (11F11)},
  MRNUMBER = {MR993107 (91b:11070)},
}

 
@book {MR993101,
     TITLE = {S\'eminaire de {T}h\'eorie des {N}ombres. 1987--1988},
      NOTE = {Held at the Universit\'e de Bordeaux I, Talence, 1987--1988},
 PUBLISHER = {Universit\'e de Bordeaux I U.E.R. de Math\'ematiques et
              d'Informatique Laboratoire de Th\'eorie des Nombres},
   ADDRESS = {Talence},
      YEAR = {19??},
     PAGES = {vi+536},
   MRCLASS = {11-06},
  MRNUMBER = {MR993101 (90a:11003)},
}



@article {cremona-lingham,
  author = {Cremona, J. and Lingham, M.\thinspace{}P.},
  title = {Finding all elliptic curves with good reduction 
outside a given set of primes},
   year = {2004},
   journal = {In Progress}
}
 
@article {rubin-silverberg:ranks,
    AUTHOR = {Rubin, K. and Silverberg, A.},
     TITLE = {Ranks of elliptic curves},
   JOURNAL = {Bull. Amer. Math. Soc. (N.S.)},
  FJOURNAL = {American Mathematical Society. Bulletin. New Series},
    VOLUME = {39},
      YEAR = {2002},
    NUMBER = {4},
     PAGES = {455--474 (electronic)},
      ISSN = {0273-0979},
     CODEN = {BAMOAD},
   MRCLASS = {11G05 (11G40)},
  MRNUMBER = {MR1920278 (2003f:11080)},
MRREVIEWER = {Ioannis Papadopoulos},
}

 
@incollection {silverberg:open_questions,
    AUTHOR = {Silverberg, A.},
     TITLE = {Open questions in arithmetic algebraic geometry},
 BOOKTITLE = {Arithmetic algebraic geometry (Park City, UT, 1999)},
    SERIES = {IAS/Park City Math. Ser.},
    VOLUME = {9},
     PAGES = {83--142},
 PUBLISHER = {Amer. Math. Soc.},
   ADDRESS = {Providence, RI},
      YEAR = {2001},
   MRCLASS = {11Gxx (14Gxx)},
  MRNUMBER = {MR1860041 (2002g:11073)},
MRREVIEWER = {Joseph H. Silverman},
}

@book {MR1860012,
     TITLE = {Arithmetic algebraic geometry},
    SERIES = {IAS/Park City Mathematics Series},
    VOLUME = {9},
    EDITOR = {Conrad, Brian and Rubin, Karl},
      NOTE = {Including papers from the Graduate Summer School of the
              Institute for Advanced Study/Park City Mathematics Institute
              held in Park City, UT, June 20--July 10, 1999},
 PUBLISHER = {American Mathematical Society},
   ADDRESS = {Providence, RI},
      YEAR = {2001},
     PAGES = {xiv+569},
      ISBN = {0-8218-2173-3},
   MRCLASS = {11-06 (14-06)},
  MRNUMBER = {MR1860012 (2002d:11003)},
}


@incollection {goldfeld:conjectures_quadratic,
    AUTHOR = {Goldfeld, D.},
     TITLE = {Conjectures on elliptic curves over quadratic fields},
 BOOKTITLE = {Number theory, Carbondale 1979 (Proc. Southern Illinois Conf.,
              Southern Illinois Univ., Carbondale, Ill., 1979)},
    SERIES = {Lecture Notes in Math.},
    VOLUME = {751},
     PAGES = {108--118},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1979},
   MRCLASS = {12A70 (14K07)},
  MRNUMBER = {MR564926 (81i:12014)},
MRREVIEWER = {Kenneth Kramer},
}

 
@proceedings {MR564918,
     TITLE = {Number theory, {C}arbondale 1979},
    SERIES = {Lecture Notes in Mathematics},
    VOLUME = {751},
 BOOKTITLE = {Proceedings of the Southern Illinois Number Theory Conference,
              held at Southern Illinois University, Carbondale, Ill., March
              30--31, 1979},
    EDITOR = {Nathanson, Melvyn B.},
 PUBLISHER = {Springer},
   ADDRESS = {Berlin},
      YEAR = {1979},
     PAGES = {iv+342},
      ISBN = {3-540-09559-4},
   MRCLASS = {10-06},
  MRNUMBER = {MR564918 (81a:10004)},
}


@article {kramarz-zagier,
    AUTHOR = {Zagier, D. and Kramarz, G.},
     TITLE = {Numerical investigations related to the {$L$}-series of
              certain elliptic curves},
   JOURNAL = {J. Indian Math. Soc. (N.S.)},
  FJOURNAL = {The Journal of the Indian Mathematical Society. New Series},
    VOLUME = {52},
      YEAR = {1987},
     PAGES = {51--69 (1988)},
      ISSN = {0019-5839},
     CODEN = {JIMTA2},
   MRCLASS = {11G05 (11G40 11Y50)},
  MRNUMBER = {MR989230 (90d:11072)},
MRREVIEWER = {M. Ram Murty},
}

@article{darmon-pollack,
  author = {Darmon, H. and Pollack, R.}, 
  title = {The efficient calculation of {S}tark-{H}eegner points
via overconvergent modular symbols},
   year = {2004}
}

@article{kraus,
  author = {Kraus, Alain},
  title = {D\'etermination du poids et du conducteur associ\'es
aux repr\'esentations des points de $p$-torsion d'une courbe elliptique}
}

@article{math252,
  author = {Stein, William},
  title = {Modular Abelian Varieties, \hfill\mbox{}
{\tt http://modular.fas.harvard.edu/edu/Fall2003/252/}},
  year = {2003}
}

@article{dembele,
  author = {Dembele, Lassina},
  title = {Quaternionic Modular Symbols and Computing {H}ilbert Modular Forms,
\hfill\mbox{}
{\tt http://modular.fas.harvard.edu/mcs/archive/Spring2004/dembele.html}},
  year = {2004}
}

@article{lemelin:dominic,
  author = {Lemelin, Dominic},
  title = {Mazur-Tate Type Conjectures for Elliptic Curves Defined over Quadratic Imaginary Fields},
  year = {2001}
}

@article{diderot:thesis,
  author = {Diderot, Denis},
  title = {P\'eriodes de formes modulaires de poids 1},
  year = {2001},
 journal = {{\tt http://modular.fas.harvard.edu/scans/papers/diderot/}}
}
  

@article{basmaji:thesis,
   author = {Basmaji, Jacques},
   TITLE = {Ein Algorithmus zur Berechnung von Hecke-Operatoren und
            Anwendungen auf modulare Kurven},
   YEAR = {1996},
   journal={{\tt http://modular.fas.harvard.edu/scans/papers/basmaji/}}
}

@article {sokurov:shimura,
    AUTHOR = {{\v{S}}okurov, V.\thinspace{}V.},
     TITLE = {Shimura integrals of cusp forms},
   JOURNAL = {Izv. Akad. Nauk SSSR Ser. Mat.},
  FJOURNAL = {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya},
    VOLUME = {44},
      YEAR = {1980},
    NUMBER = {3},
     PAGES = {670--718, 720},
      ISSN = {0373-2436},
   MRCLASS = {10D12 (14K22)},
  MRNUMBER = {MR582162 (82b:10029)},
MRREVIEWER = {K.-B. Gundlach},
}

@book {knuth2,
    AUTHOR = {Knuth, Donald E.},
     TITLE = {The art of computer programming. {V}ol. 2},
   EDITION = {Third},
      NOTE = {Seminumerical algorithms,
              Addison-Wesley Series in Computer Science and Information
              Processing},
 PUBLISHER = {Addison-Wesley Publishing Co., Reading, Mass.}
}

@Article{	  csirik-wetherell-zieve:g0,
  author	= {Csirik, Janos A. and Wetherell, Joseph L. and Zieve,
		  Michael E.},
  title		= {On the genera of {$X_0(N)$}},
  journal	= {See {\tt http://www.csirik.net/papers.html}},
  year		= {2001}
}

@Article{	  pr:exp,
  author	= {Perrin-Riou, Bernadette},
  title		= {Arithm\'etique des courbes elliptiques \`a r\'eduction
		  supersinguli\`ere en {$p$}},
  journal	= {Experiment. Math.},
  fjournal	= {Experimental Mathematics},
  volume	= {12},
  year		= {2003},
  number	= {2},
  pages		= {155--186},
  issn		= {1058-6458},
  mrclass	= {11G05},
  mrnumber	= {MR2016704}
}

@Article{	  mtt,
  author	= {Mazur, B. and Tate, J. and Teitelbaum, J.},
  title		= {On {$p$}-adic analogues of the conjectures of {B}irch and
		  {S}winnerton-{D}yer},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {84},
  year		= {1986},
  number	= {1},
  pages		= {1--48},
  issn		= {0020-9910},
  coden		= {INVMBH},
  mrclass	= {11G40 (11G05 14G10)},
  mrnumber	= {MR830037 (87e:11076)},
  mrreviewer	= {Kenneth A. Ribet}
}

@Article{	  serre:asymptotique,
  author	= {Serre, Jean-Pierre},
  title		= {R\'epartition asymptotique des valeurs propres de
		  l'op\'erateur de {H}ecke {$T\sb p$}},
  journal	= {J. Amer. Math. Soc.},
  fjournal	= {Journal of the American Mathematical Society},
  volume	= {10},
  year		= {1997},
  number	= {1},
  pages		= {75--102},
  issn		= {0894-0347},
  mrclass	= {11F30 (11F25 11G20 11N37 11R45)},
  mrnumber	= {97h:11048},
  mrreviewer	= {Glenn Stevens}
}

@Book{		  iwaniec:topics,
  author	= {Iwaniec, Henryk},
  title		= {Topics in classical automorphic forms},
  series	= {Graduate Studies in Mathematics},
  volume	= {17},
  publisher	= {American Mathematical Society},
  address	= {Providence, RI},
  year		= {1997},
  pages		= {xii+259},
  isbn		= {0-8218-0777-3},
  mrclass	= {11Fxx (11-02)},
  mrnumber	= {98e:11051},
  mrreviewer	= {B. Ramakrishnan}
}

@Article{	  gordon:dlp,
  author	= {Gordon, D.},
  year	= {2004},
  title		= {Discrete Logarithm Problem, \hfill\\ {\tt
		  http://www.win.tue.nl/\~{ }henkvt/Content.html}}
}

@Proceedings{	  mr98i:94002,
  title		= {Advances in cryptology---{EUROCRYPT} '97},
  series	= {Lecture Notes in Computer Science},
  volume	= {1233},
  booktitle	= {Proceedings of the 16th International Conference on the
		  Theory and Application of Cryptographic Techniques held in
		  Konstanz, May 11--15, 1997},
  editor	= {Fumy, Walter},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1997},
  pages		= {xii+509},
  isbn		= {3-540-62975-0},
  mrclass	= {94-06 (68P25 94A60)},
  mrnumber	= {98i:94002}
}

@Article{	  nechaev:lower,
  author	= {Nechaev, V. I.},
  title		= {On the complexity of a deterministic algorithm for a
		  discrete logarithm},
  journal	= {Mat. Zametki},
  fjournal	= {Rossi\u\i skaya Akademiya Nauk. Matematicheskie Zametki},
  volume	= {55},
  year		= {1994},
  number	= {2},
  pages		= {91--101, 189},
  issn		= {0025-567X},
  mrclass	= {11Y16},
  mrnumber	= {96a:11145}
}

@InCollection{	  shoup:lower,
  author	= {Shoup, Victor},
  title		= {Lower bounds for discrete logarithms and related
		  problems},
  booktitle	= {Advances in cryptology---EUROCRYPT '97 (Konstanz)},
  series	= {Lecture Notes in Comput. Sci.},
  volume	= {1233},
  pages		= {256--266},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1997},
  mrclass	= {94A60 (68P25 68Q25)},
  mrnumber	= {98j:94023}
}

@Article{	  gordon:dlog,
  author	= {Gordon, Daniel M.},
  title		= {Discrete logarithms in {${\rm GF}(p)$} using the number
		  field sieve},
  journal	= {SIAM J. Discrete Math.},
  fjournal	= {SIAM Journal on Discrete Mathematics},
  volume	= {6},
  year		= {1993},
  number	= {1},
  pages		= {124--138},
  issn		= {0895-4801},
  coden		= {SJDMEC},
  mrclass	= {11Y16 (11N36)},
  mrnumber	= {94d:11104},
  mrreviewer	= {Joe P. Buhler}
}

@Article{	  python,
  author	= {Rossum, Guido van},
  title		= {Python,\newline{\tt http://www.python.org}}
}

@article{        cha:vanishing,
   author       = {Cha, Byungchul},
   title        = {Vanishing of some cohomology groups and bounds for the {S}hafarevich-{T}ate groups of elliptic curves},
   journal      = {J. Number Theory.},
   year         = {2005},
   volume       = {111},
   issue        = {1},
   pages        = {154--178},
   date         = {March 2005}
}
 
@Article{	  cha:shabound,
  author	= {Cha, Byungchul},
  title		= {Vanishing of {S}ome {C}ohomology {G}roups and {B}ounds for
		  the {S}hafarevich-{T}ate {G}roups of {E}lliptic {C}urves},
  journal	= {Johns-Hopkins Ph.D. Thesis},
  year		= {2003}
}

@Article{	  cassels:7,
  author	= {Cassels, J. W. S.},
  title		= {Arithmetic on curves of genus 1. {VIII}. {O}n conjectures
		  of {B}irch and {S}winnerton-{D}yer},
  journal	= {J. Reine Angew. Math.},
  volume	= {217},
  year		= {1965},
  pages		= {180--199},
  mrclass	= {14.48 (14.49)},
  mrnumber	= {31 \#3420},
  mrreviewer	= {T. Ono}
}

@Article{	  kedlaya:counting-errata,
  author	= {Kedlaya, K.\thinspace{}S.},
  title		= {Errata for: ``{C}ounting points on hyperelliptic curves
		  using {M}onsky-{W}ashnitzer cohomology'' [{J}. {R}amanujan
		  {M}ath.\ {S}oc.\ {\bf 16} (2001), no. 4, 323--338},
  note		= {Dedicated to Professor K. S. Padmanabhan},
  journal	= {J. Ramanujan Math. Soc.},
  fjournal	= {Journal of the Ramanujan Mathematical Society},
  volume	= {18},
  year		= {2003},
  number	= {4},
  pages		= {417--418},
  issn		= {0970-1249},
  mrclass	= {14G05 (11G25 14F43 14G15)},
  mrnumber	= {2 043 934}
}

@Article{	  abbott:padic,
  author	= {Abbott, J.},
  title		= {Recovery of algebraic numbers from their $p$-adic
		  approximations},
  journal	= {Proceedings of the ACM-SIGSAM 1989 international symposium
		  on Symbolic and algebraic computation},
  pages		= {112--120},
  year		= {1989},
  isbn		= {0-89791-325-6},
  publisher	= {ACM Press, New York, NY, USA}
}

@Article{	  tate:arithmetic,
  author	= {Tate, J.},
  title		= {The arithmetic of elliptic curves},
  journal	= {Invent. Math.},
  volume	= {23},
  year		= {1974},
  pages		= {179--206},
  mrclass	= {10D05 (14G25 14K15)},
  mrnumber	= {54 \#7380},
  mrreviewer	= {A. P. Ogg}
}

@Article{	  mazur-tate:sigma,
  author	= {Mazur, B. and Tate, J.},
  title		= {The {$p$}-adic sigma function},
  journal	= {Duke Math. J.},
  fjournal	= {Duke Mathematical Journal},
  volume	= {62},
  year		= {1991},
  number	= {3},
  pages		= {663--688},
  issn		= {0012-7094},
  coden		= {DUMJAO},
  mrclass	= {11G07 (11S80)},
  mrnumber	= {93d:11059}
}

@Book{		  artin-tate:cft,
  author	= {Artin, E. and Tate, J.},
  title		= {Class field theory},
  series	= {Advanced Book Classics},
  edition	= {Second},
  publisher	= {Addison-Wesley Publishing Company Advanced Book Program},
  address	= {Redwood City, CA},
  year		= {1990},
  pages		= {xxxviii+259},
  isbn		= {0-201-51011-1},
  mrclass	= {11R37 (11-01 11R34)},
  mrnumber	= {91b:11129}
}

@Article{	  mahler:inequalities,
  author	= {Mahler, K.},
  title		= {Inequalities for ideal bases in algebraic number fields},
  journal	= {J. Austral. Math. Soc.},
  volume	= {4},
  year		= {1964},
  pages		= {425--448},
  mrclass	= {12.50},
  mrnumber	= {31 \#1243},
  mrreviewer	= {L. R. McCulloh}
}

@Article{	  iwasawa:adele,
  author	= {Iwasawa, K.},
  title		= {On the rings of valuation vectors},
  journal	= {Ann. of Math. (2)},
  volume	= {57},
  year		= {1953},
  pages		= {331--356},
  mrclass	= {10.0X},
  mrnumber	= {14,849a},
  mrreviewer	= {J. T. Tate}
}

@Book{		  lang:algebraic_numbers,
  author	= {Lang, S.},
  title		= {Algebraic numbers},
  publisher	= {Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo
		  Alto-London},
  year		= {1964},
  pages		= {ix+163},
  mrclass	= {10.65},
  mrnumber	= {28 \#3974},
  mrreviewer	= {S. Chowla}
}

@Book{		  cassels:lectures,
  author	= {Cassels, J.\thinspace{}W.\thinspace{}S.},
  title		= {Lectures on elliptic curves},
  series	= {London Mathematical Society Student Texts},
  volume	= {24},
  publisher	= {Cambridge University Press},
  address	= {Cambridge},
  year		= {1991},
  pages		= {vi+137},
  isbn		= {0-521-41517-9; 0-521-42530-1},
  mrclass	= {11G05 (14H52)},
  mrnumber	= {92k:11058},
  mrreviewer	= {Philippe Satg{\'e}}
}

@Article{	  lenstra:pell,
  author	= {Lenstra, Jr., H.\thinspace{}W.},
  title		= {Solving the {P}ell equation},
  journal	= {Notices Amer. Math. Soc.},
  fjournal	= {Notices of the American Mathematical Society},
  volume	= {49},
  year		= {2002},
  number	= {2},
  pages		= {182--192},
  issn		= {0002-9920},
  coden		= {AMNOAN},
  mrclass	= {11D09 (01A99 11R27)},
  mrnumber	= {2002i:11028},
  mrreviewer	= {Duncan A. Buell}
}

@Book{		  artin:algebra,
  author	= {Artin, M.},
  title		= {Algebra},
  publisher	= {Prentice Hall Inc.},
  address	= {Englewood Cliffs, NJ},
  year		= {1991},
  pages		= {xviii+618},
  isbn		= {0-13-004763-5},
  mrclass	= {00A05 (11-01 12-01 13-01 15-01 16-01 20-01)},
  mrnumber	= {92g:00001},
  mrreviewer	= {Gerald J. Janusz}
}

@Book{		  artin:ant,
  author	= {Artin, E.},
  title		= {Theory of algebraic numbers},
  series	= {Notes by Gerhard W\"urges from lectures held at the
		  Mathematisches Institut, G\"ottingen, Germany, in the
		  Winter Semester},
  volume	= {1956/7},
  publisher	= {George Striker, Schildweg 12, G\"ottingen},
  year		= {1959},
  pages		= {172},
  mrclass	= {10.65},
  mrnumber	= {24 \#A1884},
  mrreviewer	= {L. Carlitz}
}

@Book{		  am,
  author	= {Atiyah, M. F. and Macdonald, I. G.},
  title		= {Introduction to commutative algebra},
  publisher	= {Addison-Wesley Publishing Co., Reading, Mass.-London-Don
		  Mills, Ont.},
  year		= {1969},
  pages		= {ix+128},
  mrclass	= {13.00},
  mrnumber	= {39 \#4129},
  mrreviewer	= {J. A. Johnson}
}

@Article{	  agashe,
  author	= {Agashe, A.},
  title		= {On invisible elements of the {T}ate-{S}hafarevich group},
  journal	= {C. R. Acad. Sci. Paris S\'er. I Math.},
  fjournal	= {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I.
		  Math\'ematique},
  volume	= {328},
  year		= {1999},
  number	= {5},
  pages		= {369--374},
  issn		= {0764-4442},
  coden		= {CASMEI},
  mrclass	= {11Gxx},
  mrnumber	= {1 678 131}
}

@article {agashe-stein:bsd,
    AUTHOR = {Agashe, A. and Stein, W.},
     TITLE = {Visible evidence for the {B}irch and {S}winnerton-{D}yer
              conjecture for modular abelian varieties of analytic rank
              zero},
      NOTE = {With an appendix by J.\ Cremona and B.\ Mazur},
   JOURNAL = {Math. Comp.},
  FJOURNAL = {Mathematics of Computation},
    VOLUME = {74},
      YEAR = {2005},
    NUMBER = {249},
     PAGES = {455--484 (electronic)},
      ISSN = {0025-5718},
     CODEN = {MCMPAF},
   MRCLASS = {11G40 (11G10)},
  MRNUMBER = {2085902},
}


@Article{	  agashe-ribet-stein:manin,
  author	= "Agashe, A. and Ribet, K.\thinspace{}A. and 
                    Stein, W.\thinspace{}A.",
  title		= "The {M}anin {C}onstant, {C}ongruence {P}rimes, 
                   and the {M}odular {D}egree",
  year		= {2005},
  journal	= {Preprint,\hfill\\ {\tt
		  http://modular.fas.harvard.edu/papers/manin-agashe/}}
}
@article {lario-schoof,
    AUTHOR = {Lario, Joan-C. and Schoof, Ren{\'e}},
     TITLE = {Some computations with {H}ecke rings and deformation rings},
      NOTE = {With an appendix by Amod Agashe and William Stein},
   JOURNAL = {Experiment. Math.},
  FJOURNAL = {Experimental Mathematics},
    VOLUME = {11},
      YEAR = {2002},
    NUMBER = {2},
     PAGES = {303--311},
      ISSN = {1058-6458},
   MRCLASS = {11F80 (11F11 11F25)},
  MRNUMBER = {MR1959271 (2004b:11072)},
MRREVIEWER = {Lea Terracini},
}


@Article{	  agashe-stein:visibility,
  author	= {Agashe, A. and Stein, W.\thinspace{}A.},
  title		= {Visibility of {S}hafarevich-{T}ate groups of abelian
		  varieties},
  journal	= {J. Number Theory},
  fjournal	= {Journal of Number Theory},
  volume	= {97},
  year		= {2002},
  number	= {1},
  pages		= {171--185},
  issn		= {0022-314X},
  coden		= {JNUTA9},
  mrclass	= {11G40 (11G10 14K15)},
  mrnumber	= {2003h:11070},
  mrreviewer	= {Chandan Singh Dalawat}
}

@Article{	  agashe:invisible,
  author	= {Agash{\'e}, Amod},
  title		= {On invisible elements of the {T}ate-{S}hafarevich group},
  journal	= {C. R. Acad. Sci. Paris S\'er. I Math.},
  fjournal	= {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I.
		  Math\'ematique},
  volume	= {328},
  year		= {1999},
  number	= {5},
  pages		= {369--374},
  issn		= {0764-4442},
  coden		= {CASMEI},
  mrclass	= {11G40 (11G10 11G18)},
  mrnumber	= {2000e:11083},
  mrreviewer	= {Kenneth Kramer}
}

@Article{	  agashe:phd,
  author	= "Agashe, A.",
  title		= {The {B}irch and {S}winnerton-{D}yer formula for modular
		  abelian varieties of analytic rank~$0$},
  journal	= {Ph.D. thesis, University of California, Berkeley},
  year		= {2000}
}

@Book{		  antwerpiv,
  title		= {Modular functions of one variable. {I}{V}},
  booktitle	= {Proceedings of the International Summer School on Modular
		  Functions of One Variable and Arithmetical Applications,
		  RUCA, University of Antwerp, Antwerp, July 17--August 3,
		  1972},
  editor	= {Birch, B.\thinspace{}J. and Kuyk, W.},
  note		= {Lecture Notes in Mathematics, Vol. 476},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1975},
  pages		= {iv+151}
}

@Article{	  artin:conjecture,
  author	= {Artin, E.},
  title		= {{\"U}ber eine neue {A}rt von {L}-Reihen},
  journal	= {Abh. Math. Sem. Univ. Hamburg},
  volume	= {3},
  year		= {1923},
  pages		= {89--108}
}

@Article{	  artin:conjecture2,
  author	= {Artin, E},
  title		= {Zur {T}heorie der {L}-{R}eihen mit allgemeinen
		  {G}ruppencharakteren},
  journal	= {Abh. math. Semin. Univ. Hamburg},
  volume	= {8},
  year		= {1930},
  pages		= {292--306}
}

@Article{	  ash-stevens,
  author	= {Ash, A. and Stevens, G.},
  title		= {Cohomology of arithmetic groups and congruences between
		  systems of {H}ecke eigenvalues},
  journal	= {J. Reine Angew. Math.},
  fjournal	= {Journal f\"ur die Reine und Angewandte Mathematik},
  volume	= {365},
  year		= {1986},
  pages		= {192--220},
  issn		= {0075-4102},
  coden		= {JRMAA8}
}

@Article{	  atkin-lehner,
  author	= {Atkin, A.\thinspace{}O.\thinspace{}L. and Lehner, J.},
  title		= {Hecke operators on \protect{$\Gamma \sb{0}(m)$}},
  journal	= {Math. Ann.},
  volume	= {185},
  year		= {1970},
  pages		= {134--160}
}

@article {bdsbt,
    AUTHOR = {Buzzard, Kevin and Dickinson, Mark and Shepherd-Barron, Nick
              and Taylor, Richard},
     TITLE = {On icosahedral {A}rtin representations},
   JOURNAL = {Duke Math. J.},
  FJOURNAL = {Duke Mathematical Journal},
    VOLUME = {109},
      YEAR = {2001},
    NUMBER = {2},
     PAGES = {283--318},
      ISSN = {0012-7094},
     CODEN = {DUMJAO},
   MRCLASS = {11F80 (11F33 11G18 11R42)},
  MRNUMBER = {MR1845181 (2002k:11078)},
MRREVIEWER = {Gebhard B{\"o}ckle},
}

@Book{		  bgr,
  author	= {Bosch, S. and G{\"u}ntzer, U. and Remmert, R.},
  title		= {Non-{A}rchimedean analysis: A systematic approach to rigid
		  analytic geometry},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1984},
  pages		= {xii+436},
  isbn		= {3-540-12546-9},
  mrclass	= {32K10 (30G05 46P05)},
  mrnumber	= {86b:32031},
  mrrevr	= {W. Bartenwerfer}
}

@InCollection{	  birch:atkin,
  author	= {Birch, B.},
  title		= {Atkin and the {A}tlas {L}ab},
  booktitle	= {Proceedings of the conference in honor of
		  A.\thinspace{}O.\thinspace{}L. Atkin held at the University
		  of Illinois, Chicago, IL, September 1995},
  pages		= {13--20},
  publisher	= {Amer. Math. Soc.},
  address	= {Providence, RI},
  year		= {1998},
  mrclass	= {11-03 (01A60 11F30 11F33)},
  mrnumber	= {99c:11002},
  mrrevr	= {V. Kumar Murty}
}

@InCollection{	  birch:bsd,
  author	= {Birch, B.\thinspace{}J.},
  title		= {Elliptic curves over \protect{${\mathbf{Q}}$: {A}}
		  progress report},
  booktitle	= {1969 Number Theory Institute (Proc. Sympos. Pure Math.,
		  Vol. XX, State Univ. New York, Stony Brook, N.Y., 1969)},
  pages		= {396--400},
  publisher	= {Amer. Math. Soc.},
  address	= {Providence, R.I.},
  year		= {1971}
}

@InCollection{	  birch:cyclo,
  author	= {Birch, B.\thinspace{}J.},
  title		= {Cyclotomic fields and {K}ummer extensions},
  booktitle	= {Algebraic Number Theory (Proc. Instructional Conf.,
		  Brighton, 1965)},
  pages		= {85--93},
  publisher	= {Thompson, Washington, D.C.},
  year		= {1967}
}

@InCollection{	  birch:edsac,
  author	= {Birch, B. J.},
  title		= {Conjectures concerning elliptic curves},
  booktitle	= {Proceedings of Symposia in Pure Mathematics, VIII},
  pages		= {106--112},
  publisher	= {Amer. Math. Soc.},
  address	= {Providence, R.I.},
  year		= {1965},
  mrclass	= {14.49 (14.40)},
  mrnumber	= {30 \#4759},
  mrreviewer	= {J. W. S. Cassels}
}

@InCollection{	  birch:hecke_actions,
  author	= {Birch, B. J.},
  title		= {Hecke actions on classes of ternary quadratic forms},
  booktitle	= {Computational number theory (Debrecen, 1989)},
  pages		= {191--212},
  publisher	= {de Gruyter},
  address	= {Berlin},
  year		= {1991},
  mrclass	= {11E45 (11E20 11F11 11G05 11Y35)},
  mrnumber	= {93i:11047},
  mrrevr	= {Rainer Schulze-Pillot}
}

@InCollection{	  bloch-kato,
  author	= {Bloch, S. and Kato, K.},
  title		= {\protect{${L}$}-functions and \protect{T}amagawa numbers
		  of motives},
  booktitle	= {The Grothendieck Festschrift, Vol. \protect{I}},
  pages		= {333--400},
  publisher	= {Birkh\"auser Boston},
  address	= {Boston, MA},
  year		= {1990}
}

@Article{	  bockle:density,
  author	= {B{\"o}ckle, Gebhard},
  title		= {On the density of modular points in universal deformation
		  spaces},
  journal	= {Amer. J. Math.},
  fjournal	= {American Journal of Mathematics},
  volume	= {123},
  year		= {2001},
  number	= {5},
  pages		= {985--1007},
  issn		= {0002-9327},
  coden		= {AJMAAN},
  mrclass	= {11F80},
  mrnumber	= {1 854 117}
}

@Article{	  bolling:sha,
  author	= {B{\"o}lling, Reinhard},
  title		= {Die {O}rdnung der {S}chafarewitsch-{T}ate-{G}ruppe kann
		  beliebig gro\ss \ werden},
  journal	= {Math. Nachr.},
  volume	= {67},
  year		= {1975},
  pages		= {157--179},
  mrclass	= {14K15},
  mrnumber	= {52 \#5684},
  mrreviewer	= {J. W. S. Cassels}
}

@Proceedings{	  boston,
  title		= {Modular forms and \protect{F}ermat's last theorem
		  (Boston,MA, 1995)},
  editor	= {Cornell, G. and Silverman, J.\thinspace{}H. and Stevens,
		  G.},
  note		= {Papers from the Instructional Conference on Number Theory
		  and Arithmetic Geometry held at Boston University, Boston,
		  MA, August 9--18, 1995},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {1997},
  pages		= {xx+582},
  isbn		= {0-387-94609-8}
}

@Article{	  boston-lenstra-ribet,
  author	= {N. Boston and \protect{H.\thinspace{}W. Lenstra, Jr.} and
		  K.\thinspace{}A. Ribet},
  title		= {Quotients of group rings arising from two-dimensional
		  representations},
  journal	= {C. R. Acad. Sci. Paris S\'er. I Math.},
  fjournal	= {Comptes Rendus de l'Acad\'emie des Sciences. S\'erie I.
		  Math\'ematique},
  volume	= {312},
  year		= {1991},
  number	= {4},
  pages		= {323--328},
  issn		= {0764-4442},
  coden		= {CASMEI}
}

@Article{	  breuil-conrad-diamond-taylor,
  author	= {Breuil, C. and Conrad, B. and Diamond, F. and Taylor, R.},
  title		= {On the modularity of elliptic curves over {$\bold Q$}:
		  wild 3-adic exercises},
  journal	= {J. Amer. Math. Soc.},
  fjournal	= {Journal of the American Mathematical Society},
  volume	= {14},
  year		= {2001},
  number	= {4},
  pages		= {843--939 (electronic)},
  issn		= {0894-0347},
  mrclass	= {11G05 (11F80 11G07 14G35)},
  mrnumber	= {2002d:11058},
  mrreviewer	= {Karl Rubin}
}

@Article{	  brue,
  author	= {Brueggeman, S.},
  title		= {The non-existence of certain \protect{Galois} extensions
		  unramified outside 5},
  journal	= {Journal of Number Theory},
  volume	= {75},
  year		= {1999},
  pages		= {47--52}
}

@Article{	  brumer-mcguinness,
  author	= {Brumer, A. and McGuinness, O.},
  title		= {The behavior of the {M}ordell-{W}eil group of elliptic
		  curves},
  journal	= {Bull. Amer. Math. Soc. (N.S.)},
  fjournal	= {American Mathematical Society. Bulletin. New Series},
  volume	= {23},
  year		= {1990},
  number	= {2},
  pages		= {375--382},
  issn		= {0273-0979},
  coden		= {BAMOAD},
  note		= {Data at \protect{\tt http://oisinmc.com/math/310716/}}
}

@Article{	  brumer:rank,
  author	= {Brumer, A.},
  title		= {The rank of \protect{${J}\sb 0({N})$}},
  note		= {Columbia University Number Theory Seminar (New York,
		  1992)},
  journal	= {Ast\'erisque},
  fjournal	= {Ast\'erisque},
  number	= {228},
  year		= {1995},
  pages		= {3, 41--68},
  issn		= {0303-1179}
}

@Article{	  buhler-gross,
  author	= {Buhler, J.\thinspace{}P. and Gross, B.\thinspace{}H.},
  title		= {Arithmetic on elliptic curves with complex multiplication.
		  {I}{I}},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {79},
  year		= {1985},
  number	= {1},
  pages		= {11--29},
  issn		= {0020-9910},
  coden		= {INVMBH},
  mrclass	= {11G40 (11G05 14K22)},
  mrnumber	= {86j:11066},
  mrreviewer	= {Kenneth Kramer}
}

@Book{		  buhler:thesis,
  author	= {Buhler, J.\thinspace{}P.},
  title		= {Icosahedral \protect{G}alois representations},
  note		= {Lecture Notes in Mathematics, Vol. 654},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1978},
  pages		= {ii+143},
  isbn		= {3-540-08844-X}
}

@article {bump-friedberg-hoffstein:nonvanishing,
    AUTHOR = {Bump, Daniel and Friedberg, Solomon and Hoffstein, Jeffrey},
     TITLE = {Nonvanishing theorems for {$L$}-functions of modular forms and
              their derivatives},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {102},
      YEAR = {1990},
    NUMBER = {3},
     PAGES = {543--618},
      ISSN = {0020-9910},
     CODEN = {INVMBH},
   MRCLASS = {11F66 (11F67 11G05 11G40)},
  MRNUMBER = {MR1074487 (92a:11058)},
MRREVIEWER = {Alexey A. Panchishkin},
}

@Article{	  bump-friedberg-hoffstein,
  author	= {Bump, D. and Friedberg, S. and Hoffstein, J.},
  title		= {Eisenstein series on the metaplectic group and
		  nonvanishing theorems for automorphic
		  \protect{${L}$}-functions and their derivatives},
  journal	= {Ann. of Math. (2)},
  fjournal	= {Annals of Mathematics. Second Series},
  volume	= {131},
  year		= {1990},
  number	= {1},
  pages		= {53--127},
  issn		= {0003-486X},
  coden		= {ANMAAH}
}

@Article{	  buzzard-stein:artin,
  author	= {Buzzard, K. and Stein, W.\thinspace{}A.},
  title		= {A mod five approach to modularity of icosahedral {G}alois
		  representations},
  journal	= {Pacific J. Math.},
  fjournal	= {Pacific Journal of Mathematics},
  volume	= {203},
  year		= {2002},
  number	= {2},
  pages		= {265--282},
  issn		= {0030-8730},
  coden		= {PJMAAI},
  mrclass	= {11F80},
  mrnumber	= {2003c:11052},
  mrreviewer	= {Mark Edward Tristan Dickinson}
}

@Article{	  buzzard-taylor,
  author	= {Buzzard, K. and Taylor, R.},
  title		= {Companion forms and weight one forms},
  journal	= {Ann. of Math. (2)},
  fjournal	= {Annals of Mathematics. Second Series},
  volume	= {149},
  year		= {1999},
  number	= {3},
  pages		= {905--919},
  issn		= {0003-486X},
  coden		= {ANMAAH},
  mrclass	= {11Fxx},
  mrnumber	= {1 709 306}
}

@Article{	  buzzard:level,
  author	= {Buzzard, K.},
  title		= {On level-lowering for mod 2 representations},
  journal	= {preprint}
}

@Article{	  buzzard:t2,
  author	= {Buzzard, Kevin},
  title		= {On the eigenvalues of the {H}ecke operator {$T\sb 2$}},
  journal	= {J. Number Theory},
  fjournal	= {Journal of Number Theory},
  volume	= {57},
  year		= {1996},
  number	= {1},
  pages		= {130--132},
  issn		= {0022-314X},
  coden		= {JNUTA9},
  mrclass	= {11F25},
  mrnumber	= {96m:11033},
  mrreviewer	= {Thomas R. Shemanske}
}

@Article{	  carayol:modell,
  author	= {Carayol, H.},
  title		= {Sur les \protect{repr\'esentations} galoisiennes modulo
		  \protect{$\ell$ attach\'ees} aux formes modulaires},
  journal	= {Duke Math. J.},
  volume	= {59},
  year		= {1989},
  pages		= {785--801}
}

@Article{	  carearly,
  author	= "Carayol, H.",
  title		= {Sur les \protect{repr\'esentations}
		  \protect{$\ell$-adiques} \protect{associ\'ees} aux formes
		  modulaires de \protect{Hilbert}},
  journal	= {Ann. scient. \protect{\'Ec.} Norm. Sup., \protect{$4^{\rm
		  eb}$ s\'erie}},
  volume	= {19},
  year		= {1986},
  pages		= {409--468}
}

@InProceedings{	  casselman,
  author	= {Casselman, W.},
  title		= {On representations of \protect{${\rm {G}{L}}\sb{2}$} and
		  the arithmetic of modular curves},
  booktitle	= {Modular functions of one variable, II (Proc. Internat.
		  Summer School, Univ. Antwerp, Antwerp, 1972)},
  pages		= {107--141. Lecture Notes in Math., Vol. 349},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1973}
}

@Book{		  cassels-flynn,
  author	= {Cassels, J.\thinspace{}W.\thinspace{}S. and Flynn,
		  E.\thinspace{}V.},
  title		= {Prolegomena to a middlebrow arithmetic of curves of genus
		  \protect{$2$}},
  publisher	= {Cambridge University Press},
  address	= {Cambridge},
  year		= {1996},
  pages		= {xiv+219},
  isbn		= {0-521-48370-0},
  mrclass	= {11G30 (11Y50 14G25)},
  mrnumber	= {97i:11071},
  mrrevr	= {Joseph H. Silverman}
}

@Proceedings{	  cassels-frohlich,
  title		= {Algebraic number theory},
  booktitle	= {Proceedings of the instructional conference held at the
		  University of Sussex, Brighton, September 1--17, 1965},
  editor	= {Cassels, J.\thinspace{}W.\thinspace{}S. and
		  \protect{Fr{\"o}hlich}, A.},
  note		= {Reprint of the 1967 original},
  publisher	= {Academic Press Inc. [Harcourt Brace Jovanovich
		  Publishers]},
  address	= {London},
  year		= {1986},
  pages		= {xviii+366},
  isbn		= {0-12-163251-2}
}

@Article{	  cassels:arithmeticiii,
  author	= {Cassels, J.\thinspace{}W.\thinspace{}S.},
  title		= {{A}rithmetic on curves of genus $1$. {I}{I}{I}. {T}he
		  {T}ate-\v {S}afarevi\v c and {S}elmer groups},
  journal	= {Proc. London Math. Soc. (3)},
  volume	= {12},
  year		= {1962},
  pages		= {259--296},
  mrclass	= {14.49},
  mrnumber	= {29 \#1212}
}

@Article{	  cassels:arithmeticiv,
  author	= {Cassels, J.\thinspace{}W.\thinspace{}S.},
  title		= {Arithmetic on curves of genus \protect{$1$}. {I}{V}.
		  {P}roof of the {H}auptvermutung},
  journal	= {J. Reine Angew. Math.},
  volume	= {211},
  year		= {1962},
  pages		= {95--112}
}

@Article{	  cassels:arithmeticv,
  author	= {Cassels, J.\thinspace{}W.\thinspace{}S.},
  title		= {Arithmetic on curves of genus 1. {V}. {T}wo
		  counterexamples},
  journal	= {J. London Math. Soc.},
  volume	= {38},
  year		= {1963},
  pages		= {244--248}
}

@Article{	  cassels:bigsha,
  author	= {Cassels, J.\thinspace{}W.\thinspace{}S.},
  title		= {Arithmetic on curves of genus $1$. {V}{I}. {T}he {T}ate-\v
		  {S}afarevi\v c group can be arbitrarily large},
  journal	= {J. Reine Angew. Math.},
  volume	= {214/215},
  year		= {1964},
  pages		= {65--70},
  mrclass	= {14.49 (10.12)},
  mrnumber	= {29 \#104},
  mrreviewer	= {P. Abellanas}
}

@Article{	  cassels:diophantinecurve,
  author	= {Cassels, J.\thinspace{}W.\thinspace{}S.},
  title		= {Diophantine equations with special reference to elliptic
		  curves},
  journal	= {J. London Math. Soc.},
  volume	= {41},
  year		= {1966},
  pages		= {193--291}
}

@InCollection{	  cassels:global,
  author	= {Cassels, J.\thinspace{}W.\thinspace{}S.},
  title		= {Global fields},
  booktitle	= {Algebraic Number Theory (Proc. Instructional Conf.,
		  Brighton, 1965)},
  pages		= {42--84},
  publisher	= {Thompson, Washington, D.C.},
  year		= {1967}
}

@Article{	  cerednik,
  author	= {{\v{C}}erednik, I.\thinspace{}V.},
  title		= {Uniformization of algebraic curves by discrete arithmetic
		  subgroups of \protect{${\rm {P}{G}{L}}\sb{2}(k\sb{w})$}
		  with compact quotient spaces},
  journal	= {Mat. Sb. (N.S.)},
  volume	= {100(142)},
  year		= {1976},
  number	= {1},
  pages		= {59--88, 165}
}

@Article{	  cheryl,
  author	= {Beaver, Cheryl DeLorme},
  title		= {$5$-torsion in the {S}hafarevich-{T}ate group of a family
		  of elliptic curves},
  journal	= {J. Number Theory},
  fjournal	= {Journal of Number Theory},
  volume	= {82},
  year		= {2000},
  number	= {1},
  pages		= {25--46},
  issn		= {0022-314X},
  coden		= {JNUTA9},
  mrclass	= {11G05 (11G07)},
  mrnumber	= {2001d:11059},
  mrreviewer	= {Kenneth Kramer}
}

@Article{	  chevalley:thm,
  author	= {Chevalley, C.},
  title		= {Une d\'emonstration d'un th\'eor\`eme sur les groupes
		  alg\'ebriques},
  journal	= {J. Math. Pures Appl. (9)},
  volume	= {39},
  year		= {1960},
  pages		= {307--317},
  mrclass	= {14.50},
  mrnumber	= {23 \#A3743},
  mrreviewer	= {I. Barsotti}
}

@Book{		  cime-1997,
  author	= "Viola, C.",
  title		= "{Arithmetic theory of elliptic curves. Lectures given at
		  the 3rd session of the {C}entro {I}nternazionale
		  {M}atematico {E}stivo \protect{(CIME)}.}",
  language	= "English",
  source	= "{{L}ecture {N}otes in {M}athematics. 1716. {B}erlin:
		  {S}pringer. viii, 260 p. DM 74.00; oeS 541.00; sFr. 67.50;
		  \sterling 28.50; \$ 52.80 (1999). [ISBN 3-540-66546-3/hbk;
		  ISSN 0075-8434]}",
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1997},
  pages		= {260}
}

@Article{	  cmi:problems,
  author	= {Clay Mathematics Institute},
  title		= {Millennium Prize Problems,\hfill\\{\tt
		  http://www.claymath.org/Millennium\_Prize\_Problems/}}
}

@Article{	  coates-wiles:bsd,
  author	= {Coates, J. and Wiles, A.},
  title		= {On the conjecture of {B}irch and {S}winnerton-{D}yer},
  journal	= {Invent. Math.},
  volume	= {39},
  year		= {1977},
  number	= {3},
  pages		= {223--251},
  mrclass	= {14G10 (10D15 14G25)},
  mrnumber	= {57 \#3134},
  mrreviewer	= {Kenneth A. Ribet}
}

@Article{	  cohen-oesterle:dimensions,
  author	= {Cohen, H. and Oesterl{\'e}, J.},
  title		= {Dimensions des espaces de formes modulaires},
  booktitle	= {Modular functions of one variable, VI (Proc. Second
		  Internat. Conf., Univ. Bonn, Bonn, 1976)},
  pages		= {69--78. Lecture Notes in Math., Vol. 627},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1977},
  mrclass	= {10D15},
  mrnumber	= {57 \#12396},
  mrrevr	= {R. A. Rankin}
}

@Book{		  cohen:course_ant,
  author	= {Cohen, H.},
  title		= {A course in computational algebraic number theory},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1993},
  pages		= {xii+534},
  isbn		= {3-540-55640-0},
  mrclass	= {11Y40 (11Rxx 68Q40)},
  mrnumber	= {94i:11105},
  mrreviewer	= {Joe P. Buhler}
}

@Article{	  coleman-edixhoven,
  author	= {Coleman, R.\thinspace{}F. and Edixhoven, B.},
  title		= {On the semi-simplicity of the \protect{${U}\sb
		  p$}-operator on modular forms},
  journal	= {Math. Ann.},
  fjournal	= {Mathematische Annalen},
  volume	= {310},
  year		= {1998},
  number	= {1},
  pages		= {119--127},
  issn		= {0025-5831},
  coden		= {MAANA},
  mrclass	= {11F25 (11F11 11F33 11F85)},
  mrnumber	= {99b:11043},
  mrrevr	= {Alexey A. Panchishkin}
}

@Article{	  coleman-stein:padicapprox,
  author	= {Coleman, R.},
  title		= {Approximation of Infinite-Slope Modular Eigenforms By
		  Finite-Slope Eigenforms},
  journal	= {to appear in the Dwork Proceedings},
  year		= {2003}
}

@Article{	  coleman-voloch,
  author	= {Coleman, R.\thinspace{}F. and Voloch, J.\thinspace{}F.},
  title		= {Companion forms and \protect{K}odaira-\protect{S}pencer
		  theory},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {110},
  year		= {1992},
  number	= {2},
  pages		= {263--281},
  issn		= {0020-9910},
  coden		= {INVMBH}
}

@Article{	  coleman:banach,
  author	= {Coleman, R.\thinspace{}F.},
  title		= {$p$-adic {B}anach spaces and families of modular forms},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {127},
  year		= {1997},
  number	= {3},
  pages		= {417--479},
  issn		= {0020-9910},
  coden		= {INVMBH},
  mrclass	= {11F33 (11F67 11F85 11G07 14E30)},
  mrnumber	= {98b:11047},
  mrrevr	= {Alexey A. Panchishkin}
}

@Article{	  coleman:classical,
  author	= {Coleman, R.\thinspace{}F.},
  title		= {Classical and overconvergent modular forms},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {124},
  year		= {1996},
  number	= {1-3},
  pages		= {215--241},
  issn		= {0020-9910},
  coden		= {INVMBH},
  mrclass	= {11F85 (14G20)},
  mrnumber	= {97d:11090a},
  mrrevr	= {Fernando Q. Gouv\^ea}
}

@Article{	  coleman:classical_higher,
  author	= {Coleman, R.\thinspace{}F.},
  title		= {Classical and overconvergent modular forms of higher
		  level},
  journal	= {J. Th\'eor. Nombres Bordeaux},
  fjournal	= {Journal de Th\'eorie des Nombres de Bordeaux},
  volume	= {9},
  year		= {1997},
  number	= {2},
  pages		= {395--403},
  issn		= {1246-7405},
  mrclass	= {11F85 (11F11)},
  mrnumber	= {99g:11071},
  mrrevr	= {Conjeeveram S. Rajan}
}

@Article{	  coleman:monodromy,
  author	= {Coleman, R.},
  title		= {The {M}onodromy {P}airing},
  journal	= {Asian Math. Journal},
  volume	= {4},
  year		= {2000},
  pages		= {315--330}
}

@Article{	  coleman:serre,
  author	= {Coleman, R.\thinspace{}F.},
  title		= {Serre's conjecture: {T}he {J}ugentraum of the 20th
		  century},
  note		= {XII School of Algebra, Part I (Portuguese) (Diamantina,
		  1992)},
  journal	= {Mat. Contemp.},
  fjournal	= {Matem\'atica Contempor\cflex anea},
  volume	= {6},
  year		= {1994},
  pages		= {13--18},
  issn		= {0103-9059},
  mrclass	= {12F05 (11F03 12F12)},
  mrnumber	= {95j:12003},
  mrrevr	= {Henri Darmon}
}

@Article{	  colmez_fontaine,
  author	= {Colmez, P. and Fontaine, J.-M.},
  title		= {Construction des repr\'esentations {$p$}-adiques
		  semi-stables},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {140},
  year		= {2000},
  number	= {1},
  pages		= {1--43},
  issn		= {0020-9910},
  coden		= {INVMBH},
  mrclass	= {11S23 (14F30 14F40)},
  mrnumber	= {2001g:11184},
  mrreviewer	= {Mark Kisin}
}

@Article{	  conrad-diamond-taylor:modularity,
  author	= {Conrad, B. and Diamond, F. and Taylor, R.},
  title		= {Modularity of certain potentially
		  \protect{B}arsotti-\protect{T}ate \protect{G}alois
		  representations},
  journal	= {J. Amer. Math. Soc.},
  fjournal	= {Journal of the American Mathematical Society},
  volume	= {12},
  year		= {1999},
  number	= {2},
  pages		= {521--567},
  issn		= {0894-0347}
}

@Article{	  conrad-edixhoven-stein:j1p,
  author	= {Conrad, B. and Edixhoven, S. and Stein, W.\thinspace{}A.},
  title		= {${J}_1(p)$ {H}as {C}onnected {F}ibers},
  year		= 2003,
  journal	= {Documenta Mathematica},
  volume	= {8},
  pages		= {331--408}
}

@Article{	  conrad-stein:compgroup,
  author	= {Conrad, B. and Stein, W.\thinspace{}A.},
  title		= {Component groups of purely toric quotients},
  journal	= {Math. Res. Lett.},
  fjournal	= {Mathematical Research Letters},
  volume	= {8},
  year		= {2001},
  number	= {5-6},
  pages		= {745--766},
  issn		= {1073-2780},
  mrclass	= {11G18 (11G10 11G40 14K15)},
  mrnumber	= {2003f:11087},
  mrreviewer	= {Antoine Chambert-Loir}
}

@Article{	  conrad:eulerprod,
  author	= {Conrad, K.},
  title		= {{P}artial {E}uler products on the critical line},
  journal	= {Preprint},
  year		= {2003}
}

@InCollection{	  conrad:shimura,
  author	= {Conrad, B.},
  title		= {The Shimura Construction in Weight 2 (appendix to
		  {R}ibet-{S}tein, {L}ectures on {S}erre's {C}onjecture)},
  booktitle	= {Arithmetic algebraic geometry (Park City, UT, 1999)},
  series	= {IAS/Park City Math. Ser.},
  volume	= {9},
  pages		= {205--232},
  publisher	= {Amer. Math. Soc.},
  address	= {Providence, RI},
  year		= {2001},
  mrclass	= {11F80 (11F66 11G05)},
  mrnumber	= {2002h:11047}
}

@InCollection{	  conrey-farmer:nonvanish,
  author	= {Conrey, J.\thinspace{}B. and Farmer, D.\thinspace{}W.},
  title		= {Hecke operators and the nonvanishing of {$L$}-functions},
  booktitle	= {Topics in number theory (University Park, PA, 1997)},
  series	= {Math. Appl.},
  volume	= {467},
  pages		= {143--150},
  publisher	= {Kluwer Acad. Publ.},
  address	= {Dordrecht},
  year		= {1999},
  mrclass	= {11F67 (11F25)},
  mrnumber	= {2000f:11055},
  mrreviewer	= {Vinayak Vatsal}
}

@Article{	  cremona-luiz,
  title		= {\protect{C++} matrix classes},
  author	= {Cremona, J.\thinspace{}E. and Luiz F.}
}

@Article{	  cremona-mazur,
  author	= {Cremona, J.\thinspace{}E. and Mazur, B.},
  title		= {Visualizing elements in the {S}hafarevich-{T}ate group},
  journal	= {Experiment. Math.},
  fjournal	= {Experimental Mathematics},
  volume	= {9},
  year		= {2000},
  number	= {1},
  pages		= {13--28},
  issn		= {1058-6458},
  mrclass	= {11Gxx (14Gxx)},
  mrnumber	= {1 758 797}
}

@Book{		  cremona:algs,
  author	= {Cremona, J.\thinspace{}E.},
  title		= {Algorithms for modular elliptic curves},
  edition	= {Second},
  publisher	= {Cambridge University Press},
  address	= {Cambridge},
  year		= {1997},
  pages		= {vi+376},
  isbn		= {0-521-59820-6},
  note		= {\mbox{}\\{\tt
		  http://www.maths.nott.ac.uk/personal/jec/book/}}
}

@Article{	  cremona:gammaone,
  author	= {Cremona, J.\thinspace{}E.},
  title		= {Modular symbols for \protect{$\Gamma\sb 1({N})$} and
		  elliptic curves with everywhere good reduction},
  journal	= {Math. Proc. Cambridge Philos. Soc.},
  fjournal	= {Mathematical Proceedings of the Cambridge Philosophical
		  Society},
  volume	= {111},
  year		= {1992},
  number	= {2},
  pages		= {199--218},
  issn		= {0305-0041},
  coden		= {MPCPCO}
}

@Article{	  cremona:onlinetables,
  author	= {Cremona, J.\thinspace{}E.},
  title		= {Tables of {E}lliptic {C}urves,\hfill\\ {\tt
		  http://www.maths.nott.ac.uk/personal/jec/ftp/data/}}
}

@Article{	  cremona:periods,
  author	= {Cremona, J.\thinspace{}E.},
  title		= {Computing periods of cusp forms and modular elliptic
		  curves},
  journal	= {Experiment. Math.},
  fjournal	= {Experimental Mathematics},
  volume	= {6},
  year		= {1997},
  number	= {2},
  pages		= {97--107},
  issn		= {1058-6458}
}

@Book{		  curtis-reiner,
  author	= {Curtis, C.\thinspace{}W. and Reiner, I.},
  title		= {Representation theory of finite groups and associative
		  algebras},
  note		= {Pure and Applied Mathematics, Vol. XI},
  publisher	= {Interscience Publishers, a division of John Wiley \& Sons,
		  New York-London},
  year		= {1962},
  pages		= {xiv+685}
}

@InCollection{	  darmon-bsd,
  author	= {Darmon, H.},
  title		= {Wiles' theorem and the arithmetic of elliptic curves},
  booktitle	= {Modular forms and Fermat's last theorem (Boston, MA,
		  1995)},
  pages		= {549--569},
  publisher	= {Springer},
  address	= {New York},
  year		= {1997},
  mrclass	= {11G40 (11G05)},
  mrnumber	= {1 638 495}
}

@Article{	  darmon-merel,
  author	= {Darmon, H. and Merel, L.},
  title		= {Winding quotients and some variants of {F}ermat's last
		  theorem},
  journal	= {J. Reine Angew. Math.},
  fjournal	= {Journal f\"ur die Reine und Angewandte Mathematik},
  volume	= {490},
  year		= {1997},
  pages		= {81--100},
  issn		= {0075-4102},
  coden		= {JRMAA8},
  mrclass	= {11G18 (11D41 11F80 11G05)},
  mrnumber	= {98h:11076},
  mrrevr	= {Kenneth Kramer}
}

@InCollection{	  darmon:serre,
  author	= {Darmon, Henri},
  title		= {Serre's conjectures},
  booktitle	= {Seminar on Fermat's Last Theorem (Toronto, ON,
		  1993--1994)},
  pages		= {135--153},
  publisher	= {Amer. Math. Soc.},
  address	= {Providence, RI},
  year		= {1995},
  mrclass	= {11F80 (11F11 11R32)},
  mrnumber	= {96h:11048},
  mrrevr	= {Dipendra Prasad}
}

@InCollection{	  ddt,
  author	= {Darmon, H. and Diamond, F. and Taylor, R.},
  title		= {Fermat's last theorem},
  booktitle	= {Current developments in mathematics, 1995 (Cambridge,
		  MA)},
  pages		= {1--154},
  publisher	= {Internat. Press},
  address	= {Cambridge, MA},
  year		= {1994}
}

@InProceedings{	  deligne,
  author	= {Deligne, P.},
  title		= {Formes modulaires et \protect{repr\'{e}sentations
		  $\ell$-adiques.}},
  note		= {Lecture Notes in Mathematics, Vol. 179},
  publisher	= {Springer-Verlag},
  booktitle	= {\protect{S\'{e}m.} Bourbaki no. 355, 1968/69},
  address	= {Berlin and New York},
  year		= {1971},
  pages		= {139--172}
}

@InProceedings{	  deligne-rapoport,
  author	= {Deligne, P. and Rapoport, M.},
  title		= {Les sch\'emas de modules de courbes elliptiques},
  booktitle	= {Modular functions of one variable, II (Proc. Internat.
		  Summer School, Univ. Antwerp, Antwerp, 1972)},
  pages		= {143--316. Lecture Notes in Math., Vol. 349},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1973}
}

@Article{	  deligne-serre,
  author	= {Deligne, P. and Serre, J-P.},
  title		= {Formes modulaires de poids $1$},
  journal	= {Ann. Sci. \'Ecole Norm. Sup. (4)},
  volume	= {7},
  year		= {1974},
  pages		= {507--530 (1975)}
}

@InCollection{	  diamond-im,
  author	= {Diamond, F. and Im, J.},
  title		= {Modular forms and modular curves},
  booktitle	= {Seminar on {F}ermat's {L}ast {T}heorem},
  pages		= {39--133},
  pppublisher	= {Amer. Math. Soc.},
  address	= {Providence, RI},
  year		= {1995}
}

@Article{	  diamond-kramer,
  author	= {Diamond, F. and Kramer, K.},
  title		= {Modularity of a family of elliptic curves},
  journal	= {Math. Res. Lett.},
  fjournal	= {Mathematical Research Letters},
  volume	= {2},
  year		= {1995},
  number	= {3},
  pages		= {299--304},
  issn		= {1073-2780}
}

@InProceedings{	  diamond:refined,
  author	= {Diamond, F.},
  title		= {The refined conjecture of \protect{S}erre},
  booktitle	= {Elliptic curves, modular forms, \& \protect{F}ermat's last
		  theorem (\protect{H}ong \protect{K}ong, 1993)},
  pages		= {22--37},
  publisher	= {Internat. Press},
  address	= {Cambridge, MA},
  year		= {1995}
}

@Article{	  dickinson:thesis,
  author	= {Dickinson, M.},
  title		= {On the modularity of certain $2$-adic Galois
		  representations},
  journal	= {Harvard Ph.D. thesis},
  year		= {2000}
}

@Book{		  dixcohomologie,
  title		= {Dix expos\'es sur la cohomologie des sch\'emas},
  note		= {Advanced Studies in Pure Mathematics, Vol. 3},
  publisher	= {North-Holland Publishing Co.},
  address	= {Amsterdam},
  year		= {1968},
  pages		= {vi+386},
  mrclass	= {14.55},
  mrnumber	= {39 #2777}
}

@Article{	  doud,
  author	= {Doud, D.},
  title		= {\protect{${S}\sb 4$} and \protect{$\tilde {S}{}\sb 4$}
		  extensions of \protect{${\bf {Q}}$} ramified at only one prime},
  journal	= {J. Number Theory},
  fjournal	= {Journal of Number Theory},
  volume	= {75},
  year		= {1999},
  number	= {2},
  pages		= {185--197},
  issn		= {0022-314X},
  coden		= {JNUTA9}
}

@Article{	  drinfeld:coverings,
  author	= {Drinfeld, V.\thinspace{}G.},
  title		= {Coverings of \protect{$p$-adic} symmetric domains},
  journal	= {Funkcional. Anal. i Prilov zen.},
  volume	= {10},
  year		= {1976},
  number	= {2},
  pages		= {29--40}
}

@Article{	  dummigan-stein-watkins:motives,
  author	= {Dummigan, N. and Watkins, M. and Stein, W.\thinspace{}A.},
  title		= {{Constructing Elements in Shafarevich-Tate Groups of
		  Modular Motives}},
  journal	= {Number theory and algebraic geometry, ed. by Miles Reid
		  and Alexei Skorobogatov},
  year		= {2003},
  volume	= {303},
  series	= {Lecture Notes Series},
  publisher	= {Cambridge Univ. Press},
  pages		= {91--118}
}

@Article{	  dummigan:cp,
    AUTHOR = {Dummigan, N.},
     TITLE = {Period ratios of modular forms},
   JOURNAL = {Math. Ann.},
  FJOURNAL = {Mathematische Annalen},
    VOLUME = {318},
      YEAR = {2000},
    NUMBER = {3},
     PAGES = {621--636},
      ISSN = {0025-5831},
     CODEN = {MAANA},
   MRCLASS = {11F67 (11F33 11G40)},
  MRNUMBER = {MR1800772 (2002a:11049)},
MRREVIEWER = {Kevin L. James},
}

 
@article {dummigan:congruences,
    AUTHOR = {Dummigan, N.},
     TITLE = {Congruences of modular forms and {S}elmer groups},
   JOURNAL = {Math. Res. Lett.},
  FJOURNAL = {Mathematical Research Letters},
    VOLUME = {8},
      YEAR = {2001},
    NUMBER = {4},
     PAGES = {479--494},
      ISSN = {1073-2780},
   MRCLASS = {11F33 (11F37 11F67 11G40)},
  MRNUMBER = {MR1849264 (2002k:11064)},
MRREVIEWER = {Andrea Mori},
}


@Article{	  edixcole,
  author	= {Coleman, R.\thinspace{}F. and Edixhoven, B.},
  title		= {On the semi-simplicity of the \protect{${U}\sb
		  p$}-operator on modular forms},
  journal	= {Math. Ann.},
  fjournal	= {Mathematische Annalen},
  volume	= {310},
  year		= {1998},
  number	= {1},
  pages		= {119--127},
  issn		= {0025-5831},
  coden		= {MAANA}
}

@Article{	  edixhoven:comparison,
  author	= {Edixhoven, B.},
  title		= {Comparison of integral structures on spaces of modular
		  forms of weight two, and computation of spaces of forms
		  mod~$2$ of weight one},
  year		= {July, 2003},
  journal	= {preprint}
}

@Article{	  edixhoven:eisen,
  author	= {Edixhoven, B.},
  title		= {L'action de l'alg\`ebre de \protect{H}ecke sur les groupes
		  de composantes des jacobiennes des courbes modulaires est
		  ``\protect{E}isenstein''},
  note		= {Courbes modulaires et courbes de Shimura (Orsay,
		  1987/1988)},
  journal	= {Ast\'erisque},
  fjournal	= {Ast\'erisque},
  number	= {196--197},
  year		= {1991},
  pages		= {7--8, 159--170 (1992)},
  issn		= {0303-1179}
}

@Article{	  edixhoven:erratum,
  author	= {Edixhoven, B.},
  title		= {Erratum and addendum: ``{T}he role of {S}erre's conjecture
		  in the proof of {F}ermat's theorem''},
  journal	= {Gaz. Math.},
  fjournal	= {Gazette des Math\'ematiciens},
  number	= {67},
  year		= {1996},
  pages		= {19},
  issn		= {0224-8999},
  mrclass	= {11F33 (11D41 11F80 11G05)},
  mrnumber	= {96k:11055b},
  mrrevr	= {Fernando Q. Gouv\^ea}
}

@InCollection{	  edixhoven:manin,
  author	= {Edixhoven, B.},
  title		= {On the {M}anin constants of modular elliptic curves},
  booktitle	= {Arithmetic algebraic geometry (Texel, 1989)},
  pages		= {25--39},
  publisher	= {Birkh\"auser Boston},
  address	= {Boston, MA},
  year		= {1991},
  mrclass	= {11G05 (14G25)},
  mrnumber	= {92a:11066},
  mrreviewer	= {Philippe Satg{\'e}}
}

@Article{	  edixhoven:minimal,
  author	= {Edixhoven, B.},
  title		= {Minimal resolution and stable reduction of
		  \protect{${X}\sb 0({N})$}},
  journal	= {Ann. Inst. Fourier (Grenoble)},
  fjournal	= {Universit\'e de Grenoble. Annales de l'Institut Fourier},
  volume	= {40},
  year		= {1990},
  number	= {1},
  pages		= {31--67},
  issn		= {0373-0956},
  coden		= {AIFUA7},
  mrclass	= {11G18 (14G35)},
  mrnumber	= {92f:11080},
  mrreviewer	= {Autorreferat}
}

@InProceedings{	  edixhoven:serre,
  author	= {Edixhoven, B.},
  title		= {Serre's conjecture},
  booktitle	= {Modular forms and \protect{F}ermat's last theorem (Boston,
		  MA, 1995)},
  pages		= {209--242},
  publisher	= {Springer},
  address	= {New York},
  year		= {1997}
}

@Article{	  edixhoven:serrerole,
  author	= {Edixhoven, B.},
  title		= {Le r\^{o}le de la conjecture de {S}erre dans la
		  d\'emonstration du th\'eor\`eme de {F}ermat},
  journal	= {Gaz. Math.},
  fjournal	= {Gazette des Math\'ematiciens},
  number	= {66},
  year		= {1995},
  pages		= {25--41},
  issn		= {0224-8999},
  mrclass	= {11F33 (11D41 11F80 11G05)},
  mrnumber	= {96k:11055a},
  mrrevr	= {Fernando Q. Gouv\^ea}
}

@Article{	  edixhoven:tame,
  author	= {Edixhoven, B.},
  title		= {N\'eron models and tame ramification},
  journal	= {Compositio Math.},
  fjournal	= {Compositio Mathematica},
  volume	= {81},
  year		= {1992},
  number	= {3},
  pages		= {291--306},
  issn		= {0010-437X},
  coden		= {CMPMAF},
  mrclass	= {14K15 (11G10)},
  mrnumber	= {93a:14041},
  mrreviewer	= {Min Ho Lee}
}

@Article{	  edixhoven:weight,
  author	= {Edixhoven, B.},
  title		= {The weight in \protect{S}erre's conjectures on modular
		  forms},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {109},
  year		= {1992},
  number	= {3},
  pages		= {563--594},
  issn		= {0020-9910},
  coden		= {INVMBH}
}

@Article{	  ega4_1,
  author	= {Grothendieck, A.},
  title		= {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {I}{V}.
		  \'{E}tude locale des sch\'emas et des morphismes de
		  sch\'emas. {I}},
  journal	= {Inst. Hautes \'Etudes Sci. Publ. Math.},
  number	= {20},
  year		= {1964},
  pages		= {259},
  mrclass	= {14.05 (13.10)},
  mrnumber	= {30 \#3885},
  mrreviewer	= {H. Hironaka}
}

@Article{	  ega4_2,
  author	= {Grothendieck, A.},
  title		= {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {I}{V}.
		  \'{E}tude locale des sch\'emas et des morphismes de
		  sch\'emas. {I}{I}},
  journal	= {Inst. Hautes \'Etudes Sci. Publ. Math.},
  number	= {24},
  year		= {1965},
  pages		= {231},
  mrclass	= {14.00},
  mrnumber	= {33 \#7330},
  mrreviewer	= {H. Hironaka}
}

@Article{	  ega4_3,
  author	= {Grothendieck, A.},
  title		= {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {I}{V}.
		  \'{E}tude locale des sch\'emas et des morphismes de
		  sch\'emas. {I}{I}{I}},
  journal	= {Inst. Hautes \'Etudes Sci. Publ. Math.},
  number	= {28},
  year		= {1966},
  pages		= {255},
  mrclass	= {14.55},
  mrnumber	= {36 \#178},
  mrreviewer	= {J. P. Murre}
}

@Article{	  ega4_4,
  author	= {Grothendieck, A.},
  title		= {\'{E}l\'ements de g\'eom\'etrie alg\'ebrique. {I}{V}.
		  \'{E}tude locale des sch\'emas et des morphismes de
		  sch\'emas {I}{V}},
  journal	= {Inst. Hautes \'Etudes Sci. Publ. Math.},
  number	= {32},
  year		= {1967},
  pages		= {361},
  mrclass	= {14.55},
  mrnumber	= {39 \#220},
  mrreviewer	= {J. P. Murre}
}

@Article{	  eichler:ideal,
  author	= {Eichler, M.},
  title		= {Uber die Idealklassenzahl total definiter
		  Quaternionenalgebren},
  journal	= {Math. Zeit.},
  volume	= {43},
  year		= {1937},
  pages		= {102--109}
}

@Article{	  eichler:quadratic,
  author	= {Eichler, M.},
  title		= {Quadratische \protect{F}ormen und
		  \protect{M}odulfunktionen},
  journal	= {Acta Arith.},
  volume	= {4},
  year		= {1958},
  pages		= {217--239}
}

@InCollection{	  eigencurve,
  author	= {Coleman, R. and Mazur, B.},
  title		= {The {E}igencurve},
  booktitle	= {Galois representations in arithmetic algebraic geometry
		  (Durham, 1996)},
  pages		= {1--113},
  publisher	= {Cambridge Univ. Press},
  address	= {Cambridge},
  year		= {1998},
  mrclass	= {11Fxx (11Gxx)},
  mrnumber	= {1 696 469}
}

@Book{		  eisenbud,
  author	= {Eisenbud, D.},
  title		= {Commutative Algebra with a View Toward Algebraic
		  Geometry},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {1995},
  pages		= {xvi+785},
  isbn		= {0-387-94268-8; 0-387-94269-6},
  mrclass	= {13-01 (14A05)},
  mrnumber	= {97a:13001},
  mrrevr	= {Matthew Miller}
}

@Book{		  eisenbud-harris,
  author	= {Eisenbud, D. and Harris, J.},
  title		= {{S}chemes, {T}he language of modern algebraic geometry},
  publisher	= {Wadsworth \& Brooks/Cole Advanced Books \& Software},
  address	= {Pacific Grove, CA},
  year		= {1992},
  pages		= {xii+157},
  isbn		= {0-534-17606-2; 0-534-17604-6},
  mrclass	= {14-01 (14A15)},
  mrnumber	= {93k:14001},
  mrrevr	= {Alexey N. Rudakov}
}

@Book{		  eisenbud-harris-2,
  author	= {Eisenbud, D. and Harris, J.},
  title		= {{S}chemes, {T}he language of modern algebraic geometry},
  note		= {Graduate Texts in Mathematics, Vol.\ 197},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {},
  pages		= {}
}

@Book{		  eisenbud_harris:geometry,
  author	= {Eisenbud, D. and Harris, J.},
  title		= {The geometry of schemes},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {2000},
  pages		= {x+294},
  isbn		= {0-387-98638-3; 0-387-98637-5},
  mrclass	= {14A15 (14-01 14C05 14H50 14N05)},
  mrnumber	= {2001d:14002},
  mrreviewer	= {Allen B. Altman}
}

@InCollection{	  elkies:ffield,
  author	= {Elkies, N.\thinspace{}D.},
  title		= {Elliptic and modular curves over finite fields and related
		  computational issues},
  booktitle	= {Computational perspectives on number theory (Chicago, IL,
		  1995)},
  pages		= {21--76},
  publisher	= {Amer. Math. Soc.},
  address	= {Providence, RI},
  year		= {1998}
}

@InCollection{	  elkies:heegner,
  author	= {Elkies, N.\thinspace{}D.},
  title		= {Heegner point computations},
  booktitle	= {Algorithmic number theory (Ithaca, NY, 1994)},
  pages		= {122--133},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1994}
}

@Article{	  ellenberg-skinner:modularity,
  author	= {Ellenberg, J. and Skinner, C.},
  title		= {On the {M}odularity of {$\Q$}-curves},
  journal	= {{\tt
		  http://www.math.princeton.edu/~ellenber/papers.html\#QCURVE}}
		  ,
  year		= {2000}
}

@Article{	  ellenberg:qcurves_survey,
  author	= {Ellenberg, J.},
  title		= {$\Q$-curves and {G}alois {R}epresentations},
  journal	= {{\tt
		  http://www.math.princeton.edu/~ellenber/papers.html\#MCAV}},
  year		= {2002}
}

@Article{	  emerton:optimal,
  author	= {Emerton, M.},
  title		= {Optimal {Q}uotients of {M}odular {J}acobians},
  journal	= {preprint},
  year		= {2001}
}

@Article{	  empirical,
  author	= {Flynn, E.\thinspace{}V. and \protect{Lepr\'{e}vost}, F.
		  and Schaefer, E.\thinspace{}F. and Stein, W.\thinspace{}A.
		  and Stoll, M. and Wetherell, J.\thinspace{}L.},
  title		= {Empirical evidence for the {B}irch and {S}winnerton-{D}yer
		  conjectures for modular {J}acobians of genus 2 curves},
  journal	= {Math. Comp.},
  fjournal	= {Mathematics of Computation},
  volume	= {70},
  year		= {2001},
  number	= {236},
  pages		= {1675--1697 (electronic)},
  issn		= {0025-5718},
  coden		= {MCMPAF},
  mrclass	= {},
  mrnumber	= {1 836 926}
}

@Article{	  faltings-finiteness,
  author	= {Faltings, G.},
  title		= {\protect{Endlichkeitss\"atze f\"ur} abelsche
		  \protect{V}ariet\"aten \"uber \protect{Z}ahlk\"orpern},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {73},
  year		= {1983},
  number	= {3},
  pages		= {349--366},
  issn		= {0020-9910},
  coden		= {INVMBH}
}

@Article{	  faltings-jordan,
  author	= {Faltings, G. and Jordan, B.\thinspace{}W.},
  title		= {Crystalline cohomology and \protect{${\rm {G}{L}}(2,{\bf
		  {Q}})$}},
  journal	= {Israel J. Math.},
  fjournal	= {Israel Journal of Mathematics},
  volume	= {90},
  year		= {1995},
  number	= {1-3},
  pages		= {1--66},
  issn		= {0021-2172},
  coden		= {ISJMAP}
}

@InCollection{	  faltings:finiteness,
  author	= {Faltings, G.},
  title		= {Finiteness theorems for abelian varieties over number
		  fields},
  booktitle	= {Arithmetic geometry (Storrs, Conn., 1984)},
  pages		= {9--27},
  note		= {Translated from the German original [Invent.\ Math.\ {\bf
		  73} (1983), no.\ 3, 349--366; ibid.\ {\bf 75} (1984), no.\
		  2, 381; MR 85g:11026ab] by Edward Shipz},
  publisher	= {Springer},
  address	= {New York},
  year		= {1986},
  mrclass	= {11G10 (14K15)},
  mrnumber	= {861 971}
}

@Article{	  farmer-james:maeda,
  author	= {Farmer, D. W. and James, K.},
  title		= {The irreducibility of some level 1 {H}ecke polynomials},
  journal	= {Math. Comp.},
  fjournal	= {Mathematics of Computation},
  volume	= {71},
  year		= {2002},
  number	= {239},
  pages		= {1263--1270 (electronic)},
  issn		= {0025-5718},
  coden		= {MCMPAF},
  mrclass	= {11F25 (11F11)},
  mrnumber	= {2003e:11046},
  mrreviewer	= {T. C. Vasudevan}
}

@Article{	  fearnley:phd,
  author	= {Fearnley, J.},
  title		= {{V}anishing and {N}on-{V}anishing of {L}-Series of
		  {E}lliptic {C}urves {T}wisted by {D}irichlet {C}haracters},
  year		= 2001,
  journal	= {Concordia Ph.D. thesis}
}

@Article{	  flach:pairing,
  author	= {Flach, M.},
  title		= {A generalisation of the {C}assels-{T}ate pairing},
  journal	= {J. Reine Angew. Math.},
  fjournal	= {Journal f\"ur die Reine und Angewandte Mathematik},
  volume	= {412},
  year		= {1990},
  pages		= {113--127},
  issn		= {0075-4102},
  coden		= {JRMAA8},
  mrclass	= {11G09 (11R23 11S25)},
  mrnumber	= {92b:11037},
  mrreviewer	= {Vincent Fleckinger}
}

@Article{	  fontaine:groupes,
  author	= {Fontaine, J-M.},
  title		= {Groupes finis commutatifs sur les vecteurs de {W}itt},
  journal	= {C. R. Acad. Sci. Paris S\'er. A-B},
  volume	= {280},
  year		= {1975},
  pages		= {Ai, A1423--A1425},
  mrclass	= {14L05},
  mrnumber	= {51 \#10353},
  mrreviewer	= {Robert A. Morris}
}

@InCollection{	  frey-muller,
  author	= {Frey, G. and M{\"u}ller, M.},
  title		= {Arithmetic of modular curves and applications},
  booktitle	= {Algorithmic algebra and number theory (Heidelberg, 1997)},
  pages		= {11--48},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1999}
}

@InProceedings{	  frey:boston,
  author	= {Frey, G.},
  title		= {On ternary equations of \protect{F}ermat type and
		  relations with elliptic curves},
  booktitle	= {Modular forms and \protect{F}ermat's last theorem (Boston,
		  MA, 1995)},
  pages		= {527--548},
  publisher	= {Springer},
  address	= {New York},
  year		= {1997},
  crossref	= "boston"
}

@Book{		  freyetal,
  title		= {On {A}rtin's conjecture for odd 2-dimensional
		  representations},
  booktitle	= {On {A}rtin's conjecture for odd 2-dimensional
		  representations},
  editor	= {Frey, G.},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1994},
  pages		= {viii+148},
  isbn		= {3-540-58387-4}
}

@Article{	  freyone,
  author	= {Frey, G.},
  title		= {Links between stable elliptic curves and certain
		  {D}iophantine \protect{\nobreak{equations}}},
  journal	= {Ann. Univ. Sarav. Ser. Math.},
  fjournal	= {Annales Universitatis Saraviensis. Series Mathematicae},
  volume	= {1},
  year		= {1986},
  number	= {1},
  pages		= {iv+40}
}

@InCollection{	  freytwo,
  author	= {Frey, G.},
  title		= {Links between solutions of \protect{${A}-{B}={C}$} and
		  elliptic curves},
  booktitle	= {Number theory (Ulm, 1987)},
  pages		= {31--62},
  publisher	= {Springer},
  address	= {New York},
  year		= {1989}
}

@InCollection{	  frohlich:local,
  author	= {Fr{\"o}hlich, A.},
  title		= {Local fields},
  booktitle	= {Algebraic Number Theory (Proc. Instructional Conf.,
		  Brighton, 1965) },
  pages		= {1--41},
  publisher	= {Thompson, Washington, D.C.},
  year		= {1967}
}

@Article{	  fujiwara,
  author	= {Fujiwara, K.},
  title		= {Level optimization in the totally real case},
  journal	= {in preparation},
  year		= {1999}
}

@Article{	  galbraith,
  author	= {Galbraith, S.\thinspace{}D.},
  title		= {Equations for modular curves},
  year		= {1996},
  journal	= {Oxford Ph.D. thesis},
  pages		= {91 pp.}
}

@Article{	  ganz-lario:manin,
  author	= {Gonz\'{a}lez, J. and Lario, J-C.},
  title		= {$\mathbf{Q}$-curves and their {M}anin ideals},
  journal	= {preprint},
  year		= {2000}
}

@Article{	  generatinghecke,
  author	= "Agashe, A. and Stein, W.\thinspace{}A.",
  title		= {Generating the \protect{H}ecke algebra},
  journal	= {preprint},
  year		= {1999}
}

@Article{	  goldfeld:complexity,
  author	= {Goldfeld, D.},
  title		= {On the computational complexity of modular symbols},
  journal	= {Math. Comp.},
  fjournal	= {Mathematics of Computation},
  volume	= {58},
  year		= {1992},
  number	= {198},
  pages		= {807--814},
  issn		= {0025-5718},
  coden		= {MCMPAF},
  mrclass	= {11F67 (11Y35)},
  mrnumber	= {93a:11042},
  mrrevr	= {Glenn Stevens}
}

@Article{	  goldfeld:l1,
  author	= {Goldfeld, D.},
  title		= {Sur les produits partiels eul\'eriens attach\'es aux
		  courbes elliptiques},
  journal	= {C. R. Acad. Sci. Paris S\'er. I Math.},
  fjournal	= {Comptes Rendus des S\'eances de l'Acad\'emie des Sciences.
		  S\'erie I. Math\'ematique},
  volume	= {294},
  year		= {1982},
  number	= {14},
  pages		= {471--474},
  issn		= {0249-6321},
  coden		= {CHASAP},
  mrclass	= {14K15 (12A70 14G10 14K07)},
  mrnumber	= {84d:14031},
  mrreviewer	= {Andrew Bremner}
}

@Article{	  gonzalez-lario:manin,
  author	= {Gonz{\'a}lez, J. and Lario, J.-C.},
  title		= {{$\mathbf{Q}$}-curves and their {M}anin ideals},
  journal	= {Amer. J. Math.},
  fjournal	= {American Journal of Mathematics},
  volume	= {123},
  year		= {2001},
  number	= {3},
  pages		= {475--503},
  issn		= {0002-9327},
  coden		= {AJMAAN},
  mrclass	= {11G05 (11G18)},
  mrnumber	= {2002e:11070},
  mrreviewer	= {Ivica Gusi{\'c}}
}

@Article{	  mcgraw-ono:vis,
    AUTHOR = {McGraw, William J. and Ono, Ken},
     TITLE = {Modular form congruences and {S}elmer groups},
   JOURNAL = {J. London Math. Soc. (2)},
  FJOURNAL = {Journal of the London Mathematical Society. Second Series},
    VOLUME = {67},
      YEAR = {2003},
    NUMBER = {2},
     PAGES = {302--318},
      ISSN = {0024-6107},
     CODEN = {JLMSAK},
   MRCLASS = {11F33 (11F37 11F67 11G40)},
  MRNUMBER = {MR1956137 (2004d:11033)},
MRREVIEWER = {Vinayak Vatsal},
}

@InCollection{	  gouvea-mazur:density,
  author	= {Gouv\^{e}a, F.\thinspace{}Q. and Mazur, B.},
  title		= {On the density of modular representations},
  booktitle	= {Computational perspectives on number theory (Chicago, IL,
		  1995)},
  pages		= {127--142},
  publisher	= {Amer. Math. Soc.},
  address	= {Providence, RI},
  year		= {1998},
  mrclass	= {11F33 (11F80)},
  mrnumber	= {99a:11056},
  mrreviewer	= {Andrea Mori}
}

@Article{	  gouvea-mazur:families,
  author	= {Gouv\^ea, F. and Mazur, B.},
  title		= {Families of modular eigenforms},
  journal	= {Math. Comp.},
  fjournal	= {Mathematics of Computation},
  volume	= {58},
  year		= {1992},
  number	= {198},
  pages		= {793--805},
  issn		= {0025-5718},
  coden		= {MCMPAF},
  mrclass	= {11F33 (11Y35 14G20)},
  mrnumber	= {93d:11049},
  mrrevr	= {Bas Edixhoven}
}

@Article{	  gouvea:ordinary,
  author	= {Gouv\^ea, F.\thinspace{}Q.},
  title		= {On the ordinary {H}ecke algebra},
  journal	= {J. Number Theory},
  fjournal	= {Journal of Number Theory},
  volume	= {41},
  year		= {1992},
  number	= {2},
  pages		= {178--198},
  issn		= {0022-314X},
  coden		= {JNUTA9}
}

@Book{		  gouvea:slnm,
  author	= {Gouv\^{e}a, F.\thinspace{}Q.},
  title		= {Arithmetic of $p$-adic modular forms},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1988},
  pages		= {viii+121},
  isbn		= {3-540-18946-7},
  mrclass	= {11F85 (11F80)},
  mrnumber	= {91e:11056},
  mrreviewer	= {Alexey A. Panchishkin}
}

@Book{		  greenberg-harper,
  author	= {Greenberg, M.\thinspace{}J. and Harper, J.\thinspace{}R.},
  title		= {Algebraic topology},
  note		= {A first course},
  publisher	= {Benjamin/Cummings Publishing Co. Inc. Advanced Book
		  Program},
  address	= {Reading, Mass.},
  year		= {1981},
  pages		= {xi+311 pp. (loose errata)},
  isbn		= {0-8053-3558-7; 0-8053-3557-9},
  mrclass	= {55-01},
  mrnumber	= {83b:55001},
  mrrevr	= {J. P. May}
}

@Article{	  gross-kohnen-zagier,
  author	= {Gross, B. and Kohnen, W. and Zagier, D.},
  title		= {Heegner points and derivatives of ${L}$-series. {I}{I}},
  journal	= {Math. Ann.},
  fjournal	= {Mathematische Annalen},
  volume	= {278},
  year		= {1987},
  number	= {1-4},
  pages		= {497--562},
  issn		= {0025-5831},
  coden		= {MAANA3},
  mrclass	= {11G40 (11F30 11G05 11R29 14G10)},
  mrnumber	= {89i:11069},
  mrrevr	= {Lawrence Washington}
}

@Article{	  gross-zagier,
  author	= {Gross, B. and Zagier, D.},
  title		= {Heegner points and derivatives of \protect{${L}$}-series},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {84},
  year		= {1986},
  number	= {2},
  pages		= {225--320},
  issn		= {0020-9910},
  coden		= {INVMBH},
  mrclass	= {11G40 (11F11 11G05 14G10)},
  mrnumber	= {87j:11057},
  mrrevr	= {Loren D. Olson}
}

@InCollection{	  gross:central,
  author	= {Gross, B.\thinspace{}H.},
  title		= {${L}$-functions at the central critical point},
  booktitle	= {Motives (Seattle, WA, 1991)},
  pages		= {527--535},
  publisher	= {Amer. Math. Soc.},
  address	= {Providence, RI},
  year		= {1994},
  mrclass	= {11G40 (14G10)},
  mrnumber	= {95a:11060},
  mrrevr	= {Jan Nekov{\'a}{\v{r}}}
}

@InCollection{	  gross:kolyvagin,
  author	= {Gross, B.\thinspace{}H.},
  title		= {Kolyvagin's work on modular elliptic curves},
  booktitle	= {$L$-functions and arithmetic (Durham, 1989)},
  pages		= {235--256},
  publisher	= {Cambridge Univ. Press},
  address	= {Cambridge},
  year		= {1991}
}

@Article{	  gross:tameness,
  author	= {Gross, B.\thinspace{}H.},
  title		= {A tameness criterion for \protect{G}alois representations
		  associated to modular forms (mod \protect{$p$})},
  journal	= {Duke Math. J.},
  fjournal	= {Duke Mathematical Journal},
  volume	= {61},
  year		= {1990},
  number	= {2},
  pages		= {445--517},
  issn		= {0012-7094},
  coden		= {DUMJAO}
}

@Article{	  gross_kudla,
  author	= {Gross, B.\thinspace{}H. and Kudla, S.\thinspace{}S.},
  title		= {Heights and the central critical values of triple product
		  {$L$}-functions},
  journal	= {Compositio Math.},
  fjournal	= {Compositio Mathematica},
  volume	= {81},
  year		= {1992},
  number	= {2},
  pages		= {143--209},
  issn		= {0010-437X},
  coden		= {CMPMAF},
  mrclass	= {11F66 (11F67 11G40 19F27)},
  mrnumber	= {93g:11047},
  mrreviewer	= {Alexey A. Panchishkin}
}

@InCollection{	  grothendieck:brauer1,
  author	= {Grothendieck, Alexander},
  title		= {Le groupe de {B}rauer. {I}. {A}lg\`ebres d'{A}zumaya et
		  interpr\'etations diverses},
  booktitle	= {Dix Expos\'es sur la Cohomologie des Sch\'emas},
  pages		= {46--66},
  publisher	= {North-Holland},
  address	= {Amsterdam},
  year		= {1968},
  mrclass	= {14.55},
  mrnumber	= {39 #5586a}
}

@InCollection{	  grothendieck:brauer2,
  author	= {Grothendieck, Alexander},
  title		= {Le groupe de {B}rauer. {I}{I}. {T}h\'eorie cohomologique},
  booktitle	= {Dix Expos\'es sur la Cohomologie des Sch\'emas},
  pages		= {67--87},
  publisher	= {North-Holland},
  address	= {Amsterdam},
  year		= {1968},
  mrclass	= {14.55},
  mrnumber	= {39 #5586b}
}

@InCollection{	  grothendieck:brauer3,
  author	= {Grothendieck, Alexander},
  title		= {Le groupe de {B}rauer. {I}{I}{I}. {E}xemples et
		  compl\'ements},
  booktitle	= {Dix Expos\'es sur la Cohomologie des Sch\'emas},
  pages		= {88--188},
  publisher	= {North-Holland},
  address	= {Amsterdam},
  year		= {1968},
  mrclass	= {14.55},
  mrnumber	= {39 #5586c},
  mrrevr	= {J. S. Milne}
}

@Book{		  grothendieck:monodromie,
  author	= {Grothendieck, A.},
  title		= {Groupes de monodromie en g\'eom\'etrie alg\'ebrique.
		  \protect{I}},
  note		= {S\'eminaire de G\'eom\'etrie Alg\'ebrique du Bois-Marie
		  1967--1969 (SGA 7 I), Dirig\'e par A. Grothendieck. Avec la
		  collaboration de M. Raynaud et D. S. Rim, Lecture Notes in
		  Mathematics, Vol. 288},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1972},
  pages		= {viii+523}
}

@InCollection{	  gruenberg,
  author	= {Gruenberg, K.},
  title		= {Profinite groups},
  booktitle	= {Algebraic Number Theory (Proc. Instructional Conf.,
		  Brighton, 1965)},
  pages		= {116--127},
  publisher	= {Thompson, Washington, D.C.},
  year		= {1967}
}

@Article{	  guerzhoy:kummer,
  title		= {Searching for {K}ummer congruences in an infinite slope
		  family},
  author	= {Guerzhoy, P.},
  year		= {2000},
  journal	= {Preprint}
}

@Book{		  guy:unsolved,
  author	= {Guy, R.\thinspace{}K.},
  title		= {Unsolved problems in number theory},
  edition	= {Second},
  note		= {Unsolved Problems in Intuitive Mathematics, I},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {1994},
  pages		= {xvi+285},
  isbn		= {0-387-94289-0},
  mrclass	= {11-01 (00A07 11-02)},
  mrnumber	= {96e:11002},
  mrreviewer	= {B. M. M. de Weger}
}

@Book{		  haberland,
  author	= {Haberland, Klaus},
  title		= {Galois cohomology of algebraic number fields},
  note		= {With two appendices by Helmut Koch and Thomas Zink},
  publisher	= {VEB Deutscher Verlag der Wissenschaften},
  address	= {Berlin},
  year		= {1978},
  pages		= {145},
  mrclass	= {12A60},
  mrnumber	= {81i:12009},
  mrrevr	= {Chih-Han Sah}
}

@Book{		  halmos:naive,
  author	= {Halmos, Paul R.},
  title		= {Naive set theory},
  series	= {The University Series in Undergraduate Mathematics},
  publisher	= {D. Van Nostrand Co., Princeton, N.J.-Toronto-London-New
		  York},
  year		= {1960},
  pages		= {vii+104},
  mrclass	= {04.00},
  mrnumber	= {22 \#5575},
  mrreviewer	= {L. Rieger}
}

@Article{	  hardy_littlewood:conjf,
  author	= {Hardy, G.\thinspace{}H. and Littlewood, J.\thinspace{}E.},
  title		= {Some {P}roblems of `{P}artitio {N}umerorum.' {I}{I}{I}.
		  {O}n the {E}xpression of a {N}umber as a {S}um of
		  {P}rimes.},
  journal	= {Acta. Math.},
  volume	= {44},
  year		= {1922},
  pages		= {1--70}
}

@Book{		  hartshorne,
  author	= {Hartshorne, R.},
  title		= {Algebraic {G}eometry},
  note		= {Graduate Texts in Mathematics, No. 52},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {1977},
  pages		= {xvi+496},
  isbn		= {0-387-90244-9}
}

@Article{	  hatada:eigenvalues79,
  author	= {Hatada, K.},
  title		= {Eigenvalues of {H}ecke operators on \protect{${\rm
		  {S}{L}}(2,\,{\bf {Z}})$}},
  journal	= {Math. Ann.},
  fjournal	= {Mathematische Annalen},
  volume	= {239},
  year		= {1979},
  number	= {1},
  pages		= {75--96},
  issn		= {0025-5831},
  coden		= {MAANA3},
  mrclass	= {10D15},
  mrnumber	= {80b:10037},
  mrreviewer	= {Roy Fuller}
}

@Article{	  hatada:general,
  author	= {Hatada, K.},
  title		= {On classical and {$l$}-adic modular forms of levels
		  {$Nl\sp m$} and {$N$}},
  journal	= {J. Number Theory},
  fjournal	= {Journal of Number Theory},
  volume	= {87},
  year		= {2001},
  number	= {1},
  pages		= {1--14},
  issn		= {0022-314X},
  coden		= {JNUTA9},
  mrclass	= {11F11 (11F80 11F85)},
  mrnumber	= {2002e:11054},
  mrreviewer	= {Luis V. Dieulefait}
}

@Article{	  hatada:rationality,
  author	= {Hatada, K.},
  title		= {Multiplicity one theorem and modular symbols},
  journal	= {J. Math. Soc. Japan},
  fjournal	= {Journal of the Mathematical Society of Japan},
  volume	= {33},
  year		= {1981},
  number	= {3},
  pages		= {445--470},
  issn		= {0025-5645},
  coden		= {NISUBC},
  mrclass	= {10D12 (12A65)},
  mrnumber	= {83d:10030},
  mrrevr	= {Wen Ch'ing Winnie Li}
}

@Book{		  hellegouarch:invitation,
  author	= {Hellegouarch, Y.},
  title		= {Invitation aux math\'ematiques de {F}ermat-{W}iles},
  publisher	= {Masson},
  address	= {Paris},
  year		= {1997},
  pages		= {viii+401},
  isbn		= {2-225-83008-8},
  mrclass	= {11-01 (11D41 11F11 11G05 11G18)},
  mrnumber	= {99e:11001},
  mrrevr	= {Massimo Bertolini}
}

@Article{	  hida:invent86,
  author	= {Hida, H.},
  title		= {Galois representations into \protect{${\rm {G}{L}}\sb
		  2({\bf {Z}}\sb p[[{X}]])$} attached to ordinary cusp forms},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {85},
  year		= {1986},
  number	= {3},
  pages		= {545--613},
  issn		= {0020-9910},
  coden		= {INVMBH},
  mrclass	= {11F11 (11F33 11F85 11R23)},
  mrnumber	= {87k:11049},
  mrrevr	= {Ernst-Wilhelm Zink}
}

@Article{	  hida:iwasawa,
  author	= {Hida, H.},
  title		= {Iwasawa modules attached to congruences of cusp forms},
  journal	= {Ann. Sci. \'Ecole Norm. Sup. (4)},
  fjournal	= {Annales Scientifiques de l'\'Ecole Normale Sup\'erieure.
		  Quatri\`eme S\'erie},
  volume	= {19},
  year		= {1986},
  number	= {2},
  pages		= {231--273},
  issn		= {0012-9593},
  coden		= {ASENAH},
  mrclass	= {11F33 (11G18 11R23)},
  mrnumber	= {88i:11023},
  mrrevr	= {Yasutaka Ihara}
}

@Article{	  hida:modularity,
  author	= {Hida, H.},
  title		= {Modularity {P}roblems of {$\Q$}-{M}otives and
		  {B}ase-{C}hange},
  journal	= {Preprint, {\tt http://www.math.ucla.edu/~hida/}},
  year		= {2000}
}

@Article{	  hijikata:trace,
  author	= {Hijikata, H.},
  title		= {Explicit formula of the traces of \protect{H}ecke
		  operators for \protect{$\Gamma_0(N)$}},
  journal	= {J. Math. Soc. Japan},
  number	= {1},
  volume	= {26},
  year		= {1974},
  pages		= {56--82}
}

@Book{		  hindry-silverman:diophantine,
  author	= {Hindry, Marc and Silverman, Joseph H.},
  title		= {Diophantine geometry},
  note		= {An introduction},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {2000},
  pages		= {xiv+558},
  isbn		= {0-387-98975-7; 0-387-98981-1},
  mrclass	= {11Gxx (11-02 11G10 11G30 11G50 14G25)},
  mrnumber	= {2001e:11058},
  mrreviewer	= {Dino J. Lorenzini}
}

@InProceedings{	  hpf,
  author	= {Swinnerton-Dyer, H.\thinspace{}P.\thinspace{}F.},
  title		= {On $\ell$-adic representations and congruences for
		  coefficients of modular forms},
  booktitle	= {Proceedings of the International Summer School, University
		  of Antwerp, RUCA, July 17--August 3, 1972},
  pages		= {1--55. Lecture Notes in Math., Vol. 350},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1973}
}

@Article{	  igusa:fibre,
  author	= {Igusa, J.},
  title		= {Fibre systems of \protect{J}acobian varieties},
  journal	= {Amer. J. Math.},
  volume	= {78},
  year		= {1956},
  pages		= {171--199}
}

@Book{		  jacquet-langlands,
  author	= {Jacquet, H. and Langlands, R.\thinspace{}P.},
  title		= {Automorphic forms on \protect{${\rm {G}{L}}(2)$}},
  note		= {Lecture Notes in Mathematics, Vol. 114},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1970},
  pages		= {vii+548}
}

@Article{	  jarvis:hilbert,
  author	= {Jarvis, F.},
  title		= {On \protect{G}alois representations associated to
		  \protect{H}ilbert modular forms},
  journal	= {J. Reine Angew. Math.},
  fjournal	= {Journal f\"ur die Reine und Angewandte Mathematik},
  volume	= {491},
  year		= {1997},
  pages		= {199--216},
  issn		= {0075-4102},
  coden		= {JRMAA8}
}

@Article{	  jarvis:level,
  author	= {Jarvis, F.},
  title		= {Level lowering for modular mod \protect{$\ell$}
		  representations over totally real fields\-},
  journal	= {Math. Ann.},
  fjournal	= {Mathematische Annalen},
  volume	= {313},
  year		= {1999},
  number	= {1},
  pages		= {141--160},
  issn		= {0025-5831},
  coden		= {MAANA}
}

@Article{	  jarvis:mazur,
  author	= {Jarvis, F.},
  title		= {Mazur's principle for totally real fields of odd degree},
  journal	= {Compositio Math.},
  fjournal	= {Compositio Mathematica},
  volume	= {116},
  year		= {1999},
  number	= {1},
  pages		= {39--79},
  issn		= {0010-437X},
  coden		= {CMPMAF}
}

@InCollection{	  jochnowitz:conjecture,
  author	= {Jochnowitz, N.},
  title		= {A $p$-adic conjecture about derivatives of ${L}$-series
		  attached to modular forms},
  booktitle	= {$p$-adic monodromy and the {B}irch and {S}winnerton-{D}yer
		  conjecture},
  pages		= {239--263},
  publisher	= {Amer. Math. Soc.},
  address	= {Providence, RI},
  year		= {1994},
  mrclass	= {11F33 (11F67 11F85 11G40)},
  mrnumber	= {95g:11037},
  mrrevr	= {Andrea Mori}
}

@Article{	  jochnowitz:duke,
  author	= {Jochnowitz, N.},
  title		= {The index of the {H}ecke ring, ${T}\sb{k}$, in the ring of
		  integers of \protect{${T}\sb{k}\otimes {\bf {Q}}$}},
  journal	= {Duke Math. J.},
  fjournal	= {Duke Mathematical Journal},
  volume	= {46},
  year		= {1979},
  number	= {4},
  pages		= {861--869},
  issn		= {0012-7094},
  coden		= {DUMJAO},
  mrclass	= {10D12},
  mrnumber	= {80k:10023},
  mrrevr	= {Henri Cohen}
}

@Article{	  jochnowitz:local,
  author	= {Jochnowitz, N.},
  title		= {A study of the local components of the \protect{H}ecke
		  algebra mod \protect{$\ell$}},
  journal	= {Trans. Amer. Math. Soc.},
  fjournal	= {Transactions of the American Mathematical Society},
  volume	= {270},
  year		= {1982},
  number	= {1},
  pages		= {253--267},
  issn		= {0002-9947},
  coden		= {TAMTAM}
}

@Article{	  jones:thesis,
  author	= {Jones, D.\thinspace{}M.},
  title		= {On modular {G}alois representations in characteristic
		  $3$},
  year		= {1998},
  journal	= {U.\thinspace{}C. Berkeley Ph.D. thesis}
}

@Article{	  jordan-livne:epsilon,
  author	= {Jordan, B.\thinspace{}W. and Livn{\'e}, R.},
  title		= {Conjecture ``epsilon'' for weight \protect{$k>2$}},
  journal	= {Bull. Amer. Math. Soc. (N.S.)},
  fjournal	= {American Mathematical Society. Bulletin. New Series},
  volume	= {21},
  year		= {1989},
  number	= {1},
  pages		= {51--56},
  issn		= {0273-0979},
  coden		= {BAMOAD}
}

@Article{	  jordan-livne:sha,
  author	= {Jordan, B.\thinspace{}W. and Livn{\'e}, R.},
  title		= {On {A}tkin-{L}ehner quotients of {S}himura curves},
  journal	= {Bull. London Math. Soc.},
  fjournal	= {The Bulletin of the London Mathematical Society},
  volume	= {31},
  year		= {1999},
  number	= {6},
  pages		= {681--685},
  issn		= {0024-6093},
  coden		= {LMSBBT},
  mrclass	= {11G18 (11G10 14G35)},
  mrnumber	= {2000j:11090},
  mrreviewer	= {Chandrashekhar Khare}
}

@Article{	  joshi,
  author	= {Joshi, K.},
  title		= {Remarks on methods of {F}ontaine and {F}altings},
  journal	= {Internat. Math. Res. Notices},
  fjournal	= {International Mathematics Research Notices},
  volume	= {1999},
  number	= {22},
  pages		= {1199--1209},
  issn		= {1073-7928},
  mrclass	= {11Fxx},
  mrnumber	= {1 731 472}
}

@InProceedings{	  jps,
  author	= {Serre, J-P.},
  title		= {Congruences et formes modulaires [d'apr\`es
		  {H}.\thinspace{}{P}.\thinspace{}{F}.\ {S}winnerton-{D}yer]},
  booktitle	= {S\'eminaire Bourbaki, 24e ann\'ee (1971/1972), Exp. No.
		  416},
  pages		= {319--338. Lecture Notes in Math., Vol. 317},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1973}
}

@article {kato:secret,
    AUTHOR = {Kato, Kazuya},
     TITLE = {{$p$}-adic {H}odge theory and values of zeta functions of
              modular forms},
      NOTE = {Cohomologies $p$-adiques et applications arithm\'etiques. III},
   JOURNAL = {Ast\'erisque},
  FJOURNAL = {Ast\'erisque},
    NUMBER = {295},
      YEAR = {2004},
     PAGES = {ix, 117--290},
      ISSN = {0303-1179},
   MRCLASS = {11F85 (11F67 11G40 11R33 11S80 14G10 14G35)},
  MRNUMBER = {MR2104361},
}


@Article{	  katz:annals75,
  author	= {Katz, N.\thinspace{}M.},
  title		= {Higher congruences between modular forms},
  journal	= {Ann. of Math. (2)},
  volume	= {101},
  year		= {1975},
  pages		= {332--367},
  mrclass	= {10D05 (14K15)},
  mrnumber	= {54 #5120},
  mrrevr	= {Neal Koblitz}
}

@InProceedings{	  katz:antwerp350,
  author	= {Katz, N.\thinspace{}M.},
  title		= {$p$-adic properties of modular schemes and modular forms},
  booktitle	= {Modular functions of one variable, III (Proc. Internat.
		  Summer School, Univ. Antwerp, Antwerp, 1972)},
  pages		= {69--190. Lecture Notes in Mathematics, Vol. 350},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1973}
}

@Article{	  katz:torsion,
  author	= {Katz, N.\thinspace{}M.},
  title		= {Galois properties of torsion points on abelian varieties},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {62},
  year		= {1981},
  number	= {3},
  pages		= {481--502},
  issn		= {0020-9910},
  coden		= {INVMBH},
  mrclass	= {14K15 (10D35 14G05)},
  mrnumber	= {82d:14025},
  mrreviewer	= {Kenneth A. Ribet}
}

@InProceedings{	  katzbonn,
  author	= {Katz, N.\thinspace{}M.},
  title		= {A result on modular forms in characteristic $p$},
  booktitle	= {Modular functions of one variable, V (Proc. Second
		  Internat. Conf., Univ. Bonn, Bonn, 1976)},
  pages		= {53--61. Lecture Notes in Math., Vol. 601},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1977}
}

@Book{		  katzmazur,
  author	= {Katz, N.\thinspace{}M. and Mazur, B.},
  title		= {Arithmetic moduli of elliptic curves},
  publisher	= {Princeton University Press},
  address	= {Princeton, N.J.},
  year		= {1985},
  pages		= {xiv+514},
  isbn		= {0-691-08349-5, 0-691-08352-5}
}

@Article{	  khare:manu,
  author	= {Khare, C.},
  title		= {Multiplicities of mod $p$ {G}alois representations},
  journal	= {Manuscripta Math.},
  fjournal	= {Manuscripta Mathematica},
  volume	= {95},
  year		= {1998},
  number	= {2},
  pages		= {181--188},
  issn		= {0025-2611},
  coden		= {MSMHB2},
  mrclass	= {11F80 (11F33 11G18)},
  mrnumber	= {98m:11046},
  mrrevr	= {Ian Kiming}
}

@Article{	  klenke:phd,
  author	= "Klenke, T.",
  title		= {Modular {V}arieties and {V}isibility},
  journal	= {Ph.D. thesis, Harvard University},
  year		= {2001}
}

@Book{		  knapp:elliptic,
  author	= {Knapp, A.\thinspace{}W.},
  title		= {Elliptic curves},
  publisher	= {Princeton University Press},
  address	= {Princeton, NJ},
  year		= {1992},
  pages		= {xvi+427},
  isbn		= {0-691-08559-5}
}

@Book{		  koblitz:cong,
  author	= {Koblitz, N.},
  title		= {Introduction to elliptic curves and modular forms},
  series	= {Graduate Texts in Mathematics},
  volume	= {97},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {1984},
  pages		= {viii+248},
  isbn		= {0-387-96029-5},
  mrclass	= {11G05 (11G40 14G25 14K07)},
  mrnumber	= {86c:11040},
  mrreviewer	= {Leslie Jane Federer}
}

@InProceedings{	  kohel-stein:ants4,
  author	= "Kohel, D.\thinspace{}R. and Stein, W.\thinspace{}A.",
  title		= "Component {G}roups of {Q}uotients of \protect{$J_0(N)$}",
  booktitle	= {Proceedings of the 4th International Symposium (ANTS-IV),
		  Leiden, Netherlands, July 2--7, 2000},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {2000}
}

@Article{	  kohel:computing,
  author	= "Kohel, D.\thinspace{}R.",
  title		= "Computing modular curves via quaternions",
  journal	= "Fourth CANT Conference",
  year		= 1997
}

@Article{	  kohel:hecke,
  author	= "Kohel, D.\thinspace{}R.",
  title		= "Hecke Module Structure of Quaternions",
  journal	= "In K. Miyake, ed., {\em Class Field Theory -- Its
		  Centenary and Prospect}, The Advanced Studies in Pure
		  Mathematics Series, Math Soc. Japan."
}

@Article{	  koike:conjtwist,
  author	= "Koike, M.",
  title		= "On certain abelian varieties obtained from new forms of
		  weight $2$ on \protect{$\Gamma_0(3^4)$ and
		  $\Gamma_0(3^5)$}",
  journal	= {Nogoya Math. J.},
  volume	= {62},
  year		= {1976},
  pages		= {29--39}
}

@Article{	  kolyvagin-logachev:finiteness,
  author	= {Kolyvagin, V.\thinspace{}A. and Logachev, D.\thinspace{}Y.},
  title		= {Finiteness of the \protect{S}hafarevich-\protect{T}ate
		  group and the group of rational points for some modular
		  abelian varieties},
  journal	= {Algebra i Analiz},
  fjournal	= {Algebra i Analiz},
  volume	= {1},
  year		= {1989},
  number	= {5},
  pages		= {171--196},
  issn		= {0234-0852}
}

@Article{	  kolyvagin-logachev:totallyreal,
  author	= "Kolyvagin, V.\thinspace{}A. and Logachev,
		  D.\thinspace{}Y.",
  title		= "Finiteness of \protect{$\Sha$} over totally real fields",
  journal	= {Math. USSR Izvestiya},
  volume	= {39},
  year		= {1992},
  number	= {1},
  pages		= {829--853}
}

@InCollection{	  kolyvagin:euler_systems,
  author	= {Kolyvagin, V. A.},
  title		= {Euler systems},
  booktitle	= {The Grothendieck Festschrift, Vol.\ II},
  pages		= {435--483},
  publisher	= {Birkh\"auser Boston},
  address	= {Boston, MA},
  year		= {1990},
  mrclass	= {11R34 (11G05 11G40 11R29)},
  mrnumber	= {92g:11109},
  mrreviewer	= {Karl Rubin}
}

@InProceedings{	  kolyvagin:mordellweil,
  author	= {Kolyvagin, V.\thinspace{}A.},
  title		= {On the {M}ordell-{W}eil group and the {S}hafarevich-{T}ate
		  group of modular elliptic curves},
  booktitle	= {Proceedings of the International Congress of
		  Mathematicians, Vol.\ I, II (Kyoto, 1990)},
  pages		= {429--436},
  publisher	= {Math. Soc. Japan},
  address	= {Tokyo},
  year		= {1991},
  mrclass	= {11G40 (11G05 14G10)},
  mrnumber	= {93c:11046},
  mrrevr	= {John Jones}
}

@Article{	  kolyvagin:structure_of_selmer,
  author	= {Kolyvagin, V. A.},
  title		= {On the structure of {S}elmer groups},
  journal	= {Math. Ann.},
  fjournal	= {Mathematische Annalen},
  volume	= {291},
  year		= {1991},
  number	= {2},
  pages		= {253--259},
  issn		= {0025-5831},
  coden		= {MAANA},
  mrclass	= {11G05 (11G40)},
  mrnumber	= {93e:11073},
  mrreviewer	= {Massimo Bertolini}
}

@InCollection{	  kolyvagin:structureofsha,
  author	= {Kolyvagin, V.\thinspace{}A.},
  title		= {On the structure of {S}hafarevich-{T}ate groups},
  booktitle	= {Algebraic geometry (Chicago, IL, 1989)},
  pages		= {94--121},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1991}
}

@Article{	  kolyvagin:subclass,
  author	= {Kolyvagin, V. A.},
  title		= {Finiteness of ${E}(\mathbf{Q})$ and ${\Sha}({E},\mathbf{Q})$
		  for a subclass of {W}eil curves},
  journal	= {Izv. Akad. Nauk SSSR Ser. Mat.},
  fjournal	= {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya},
  volume	= {52},
  year		= {1988},
  number	= {3},
  pages		= {522--540, 670--671},
  issn		= {0373-2436},
  mrclass	= {11G05 (11G40 14G25 14K07)},
  mrnumber	= {89m:11056},
  mrreviewer	= {Reinhard B{\"o}lling}
}

@Article{	  kolyvagin:weil,
  author	= {Kolyvagin, V. A.},
  title		= {The {M}ordell-{W}eil and {S}hafarevich-{T}ate groups for
		  {W}eil elliptic curves},
  journal	= {Izv. Akad. Nauk SSSR Ser. Mat.},
  fjournal	= {Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya},
  volume	= {52},
  year		= {1988},
  number	= {6},
  pages		= {1154--1180, 1327},
  issn		= {0373-2436},
  mrclass	= {11G05 (11D41 11G40 14G25 14K07)},
  mrnumber	= {90f:11035},
  mrreviewer	= {Reinhard B{\"o}lling}
}

@Article{	  kramer:largesha,
  author	= {Kramer, K.},
  title		= {A family of semistable elliptic curves with large
		  {T}ate-{S}hafarevitch groups},
  journal	= {Proc. Amer. Math. Soc.},
  fjournal	= {Proceedings of the American Mathematical Society},
  volume	= {89},
  year		= {1983},
  number	= {3},
  pages		= {379--386},
  issn		= {0002-9939},
  coden		= {PAMYAR},
  mrclass	= {14K07 (11G05 14G25)},
  mrnumber	= {85d:14059},
  mrreviewer	= {Reinhard B{\"o}lling}
}

@Book{		  kubert-lang,
  author	= {Kubert, D.\thinspace{}S. and Lang, S.},
  title		= {Modular units},
  series	= {Grundlehren der Mathematischen Wissenschaften [Fundamental
		  Principles of Mathematical Science]},
  volume	= {244},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {1981},
  pages		= {xiii+358},
  isbn		= {0-387-90517-0},
  mrclass	= {12A45 (10D05 14G25)},
  mrnumber	= {84h:12009},
  mrreviewer	= {Roland Gillard}
}

@Article{	  lang-tate,
  author	= {Lang, S. and Tate, J.},
  title		= {Principal homogeneous spaces over abelian varieties},
  journal	= {Amer. J. Math.},
  volume	= {80},
  year		= {1958},
  pages		= {659--684}
}

@Book{		  lang:algebra,
  author	= {Lang, S.},
  title		= {Algebra},
  edition	= {Third},
  publisher	= {Addison-Wesley Publishing Co., Reading, Mass.},
  year		= {1993},
  pages		= {xv+912},
  isbn		= {0-201-55540-9}
}

@Book{		  lang:ant,
  author	= {Lang, S.},
  title		= {Algebraic number theory},
  edition	= {Second},
  publisher	= {Springer-Verlag},
  address	= {New York},
  year		= {1994},
  pages		= {xiv+357},
  isbn		= {0-387-94225-4}
}

@Article{	  lang:finitefields,
  author	= {Lang, S.},
  title		= {Algebraic groups over finite fields},
  journal	= {Amer. J. Math.},
  volume	= {78},
  year		= {1956},
  pages		= {555--563},
  mrclass	= {14.0X},
  mrnumber	= {19,174a},
  mrreviewer	= {P. Roquette}
}

@Book{		  lang:modular,
  author	= {Lang, S.},
  title		= {Introduction to modular forms},
  note		= {With appendixes by D. Zagier and W. Feit, Corrected
		  reprint of the 1976 original},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1995},
  pages		= {x+261},
  isbn		= {3-540-07833-9}
}

@Book{		  lang:nt3,
  author	= {Lang, S.},
  title		= {Number theory. {I}{I}{I}},
  note		= {Diophantine geometry},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1991},
  pages		= {xiv+296},
  isbn		= {3-540-53004-5},
  mrclass	= {11Gxx (14Gxx)},
  mrnumber	= {93a:11048},
  mrreviewer	= {Joseph H. Silverman}
}

@InProceedings{	  langlands:antwerp2,
  author	= {Langlands, R.\thinspace{}P.},
  title		= {Modular forms and $\ell $-adic representations},
  booktitle	= {Proceedings of the International Summer School, University
		  of Antwerp, RUCA, July 17--August 3, 1972},
  editor	= {Deligne, P. and Kuyk, W.},
  pages		= {361--500. Lecture Notes in Math., Vol. 349},
  publisher	= {Springer},
  address	= {Berlin},
  year		= {1973},
  mrclass	= {12A70 (10D15 14G10 22E50)},
  mrnumber	= {50 #7095},
  mrrevr	= {I. I. Pjateckii-Sapiro}
}

@Book{		  langlands:basechange,
  author	= {Langlands, R.\thinspace{}P.},
  title		= {Base change for \protect{${\rm {G}{L}}(2)$}},
  publisher	= {Princeton University Press},
  address	= {Princeton, N.J.},
  year		= {1980},
  pages		= {vii+237},
  isbn		= {0-691-08263-4; 0-691-08272-3}
}

@Article{	  lenstra-oort:additive,
  author	= {Lenstra, Jr., H. W. and Oort, F.},
  title		= {Abelian varieties having purely additive reduction},
  journal	= {J. Pure Appl. Algebra},
  fjournal	= {Journal of Pure and Applied Algebra},
  volume	= {36},
  year		= {1985},
  number	= {3},
  pages		= {281--298},
  issn		= {0022-4049},
  coden		= {JPAAA2},
  mrclass	= {14K15 (11G10 14G20)},
  mrnumber	= {86e:14020},
  mrreviewer	= {Joseph H. Silverman}
}

@InCollection{	  lenstra-smit:explicit,
  author	= {de Smit, B. and Lenstra, H.\thinspace{}W.,Jr.},
  title		= {Explicit construction of universal deformation rings},
  booktitle	= {Modular forms and \protect{F}ermat's last theorem (Boston,
		  MA, 1995)},
  pages		= {313--326},
  publisher	= {Springer},
  address	= {New York},
  year		= {1997}
}

@Book{		  lenstras:nfs,
  title		= {The development of the number field sieve},
  editor	= {Lenstra, A.\thinspace{}K. and Lenstra, Jr.,
		  H.\thinspace{}W.},
  publisher	= {Springer-Verlag},
  address	= {Berlin},
  year		= {1993},
  pages		= {viii+131},
  isbn		= {3-540-57013-6},
  mrclass	= {11Yxx (11-06 11N35 11N36 11Y05 11Y40)},
  mrnumber	= {96m:11116},
  mrreviewer	= {Samuel S. Wagstaff, Jr.}
}

@Article{	  lichtenbaum:curves,
  author	= {Lichtenbaum, Stephen},
  title		= {Curves over discrete valuation rings},
  journal	= {Amer. J. Math.},
  volume	= {90},
  year		= {1968},
  pages		= {380--405},
  mrclass	= {14.20},
  mrnumber	= {37 \#6284},
  mrreviewer	= {J.-E. Bertin}
}

@Article{	  lichtenbaum:duality,
  author	= {Lichtenbaum, S.},
  title		= {Duality theorems for curves over \protect{$p$}-adic
		  fields},
  journal	= {Invent. Math.},
  volume	= {7},
  year		= {1969},
  pages		= {120--136}
}

@Article{	  lidia,
  title		= {\protect{LiDIA: C++} number theory library},
  author	= {Buchmann, J.}
}

@Article{	  livne:conductors,
  author	= {Livn{\'e}, R.},
  title		= {On the conductors of mod \protect{$\ell$} \protect{G}alois
		  representations coming from modular forms},
  journal	= {J. Number Theory},
  fjournal	= {Journal of Number Theory},
  volume	= {31},
  year		= {1989},
  number	= {2},
  pages		= {133--141},
  issn		= {0022-314X},
  coden		= {JNUTA9}
}

@Proceedings{	  lms254,
  title		= {Galois Representations in Arithmetic Algebraic Geometry},
  booktitle	= {Galois Representations in Arithmetic Algebraic Geometry},
  editor	= {Scholl A.\thinspace{}J. and Taylor R.\thinspace{}L.},
  pages		= {493},
  year		= {1998},
  publisher	= {Cambridge University Press}
}

@Article{	  lorenzini:abvarred,
  author	= {Lorenzini, D.\thinspace{}J.},
  title		= "On the Jacobian of the Modular Curve \protect{$X_0(N)$}",
  journal	= "preprint"
}

@Article{	  lorenzini:compgrp,
  author	= {Lorenzini, D.\thinspace{}J.},
  title		= {On the group of components of a \protect{N}\'eron model},
  journal	= {J. Reine Angew. Math.},
  fjournal	= {Journal f\"ur die Reine und Angewandte Mathematik},
  volume	= {445},
  year		= {1993},
  pages		= {109--160},
  issn		= {0075-4102},
  coden		= {JRMAA8}
}

@Article{	  magma,
  author	= {Bosma, W. and Cannon, J. and Playoust, C.},
  title		= {The {M}agma algebra system. {I}. {T}he user language},
  note		= {Computational algebra and number theory (London, 1993)},
  journal	= {J. Symbolic Comput.},
  fjournal	= {Journal of Symbolic Computation},
  volume	= {24},
  year		= {1997},
  number	= {3--4},
  pages		= {235--265},
  issn		= {0747-7171},
  mrclass	= {68Q40},
  mrnumber	= {1 484 478}
}

@Article{	  manin:cyclo,
  author	= {Manin, J.\thinspace{}I.},
  title		= {Cyclotomic fields and modular curves},
  journal	= {Russian Math. Surveys},
  volume	= {26},
  year		= {1971},
  number	= {6},
  pages		= {7--78}
}

@Article{	  manin:parabolic,
  author	= {Manin, J.\thinspace{}I.},
  title		= {Parabolic points and zeta functions of modular curves},
  journal	= {Izv. Akad. Nauk SSSR Ser. Mat.},
  volume	= {36},
  year		= {1972},
  pages		= {19--66},
  mrclass	= {14G10 (10D15 14H25)},
  mrnumber	= {47 \#3396},
  mrrevr	= {K.-B. Gundlach}
}

@Book{		  matsumura,
  author	= {Matsumura, H.},
  title		= {Commutative ring theory},
  note		= {Translated from the Japanese by M. Reid},
  publisher	= {Cambridge University Press},
  address	= {Cambridge},
  year		= {1986},
  pages		= {xiv+320},
  isbn		= {0-521-25916-9},
  mrclass	= {13-01},
  mrnumber	= {88h:13001},
  mrreviewer	= {W. V. Vasconcelos}
}

@Article{	  mazur-ribet,
  author	= {Mazur, B. and Ribet, K.\thinspace{}A.},
  title		= {Two-dimensional representations in the arithmetic of
		  modular curves},
  note		= {Courbes modulaires et courbes de Shimura (Orsay,
		  1987/1988)},
  journal	= {Ast\'erisque},
  fjournal	= {Ast\'erisque},
  number	= {196-197},
  year		= {1991},
  pages		= {6, 215--255 (1992)},
  issn		= {0303-1179}
}

@Article{	  mazur-sd,
  author	= {Mazur, B. and Swinnerton-Dyer, P.},
  title		= {Arithmetic of {W}eil curves},
  journal	= {Invent. Math.},
  volume	= {25},
  year		= {1974},
  pages		= {1--61},
  mrclass	= {14G05 (10D05)},
  mrnumber	= {50 #7152},
  mrrevr	= {J. S. Milne}
}

@Article{	  mazur-swinnerton-dyer:arithmetic,
  author	= {Mazur, B. and Swinnerton-Dyer, P.},
  title		= {Arithmetic of {W}eil curves},
  journal	= {Invent. Math.},
  volume	= {25},
  year		= {1974},
  pages		= {1--61},
  mrclass	= {14G05 (10D05)},
  mrnumber	= {50 \#7152},
  mrreviewer	= {J. S. Milne}
}

@Article{	  mazur:arithmetic_values,
  author	= {Mazur, B.},
  title		= {On the arithmetic of special values of ${L}$\ functions},
  journal	= {Invent. Math.},
  fjournal	= {Inventiones Mathematicae},
  volume	= {55},
  year		= {1979},
  number	= {3},
  pages		= {207--240},
  issn		= {0020-9910},
  coden		= {INVMBH},
  mrclass	= {14G10 (10D24 12A70 14G25 14K07)},
  mrnumber	= {82e:14033},
  mrrevr	= {V. V. Shokurov}
}

@Article{	  mazur:arizona,
  author	= "Mazur, B.",
  title		= "Three lectures about the arithmetic of elliptic curves.",
  journal	= "To appear in the proceedings from the Arizona Southwest
		  Geometry Winter School",
  year		= 1998
}

@InCollection{	  mazur:deforming,
  author	= {Mazur, B.},
  title		= {Deforming \protect{G}alois representations},
  booktitle	= {Galois groups over \protect{${\bf Q}$} (Berkeley, CA,
		  1987)},
  pages		= {385--437},
  publisher	= {Springer},
  address	= {New York},
  year		= {1989}
}

@Article{	  mazur:eisenstein,
  author	= {Mazur, B.},
  title		= {Modular curves and the \protect{Eisenstein} ideal},
  journal	= {Inst. Hautes \'Etudes Sci. Publ. Math.},
  fjournal	= {Institut des Hautes \'Etudes Scientifiques. Publications
		  Math\'ematiques},
  number	= {47},
  year		= {1977},
  pages		= {33--186 (1978)},
  issn		= {0073-8301},
  coden		= {PMIHA6}
}

@Article{	  mazur:infinite_fern,
  author	= {Mazur, B.},
  title		= {An ``infinite fern'' in the universal deformation space of
		  {G}alois representations},
  note		= {Journ\'ee