Publications

William A. Stein

My publications are listed below; many have been published or at least accepted for publication, and each is available here. You might also want to look at some of my rougher papers, notes for somes talks, and my journal copyright gossip page.
Download MathSciNet reviews of all my papers: PDF, DVI, or HTML.
  1. Heegner Points on Rank Two Elliptic Curves (Preliminary Version), 2010.
  2. The Modular Degree, Congruence Primes and Multiplicity One, with Amod Agashe and Ken Ribet (16 pages), 2009, to appear in a volume in honor of Serge Lang.
  3. Toward a Generalization of the Gross-Zagier Conjecture (17 pages), 2009, submitted.
  4. Fast Computation of Hermite Normal Forms of Random Integer Matrices (19 pages), with Clement Pernet, 2009 (submitted).
  5. Elementary Number Theory: Primes, Congruences, and Secrets (book), 2008 published by Springer-Verlag
  6. Three Lectures about Explicit Methods in Number Theory Using Sage (38 pages), 2008.
  7. Computations About Tate-Shafarevich Groups Using Iwasawa Theory (37 pages), with Christian Wuthrich, 2008.
  8. On the generation of the coefficient field of a newform by a single Hecke eigenvalue, with Koopa Koo and Gabor Wiese (11 pages), appeared in Journal de Theorie des Nombres de Bordeaux 20 (2008), 373-384.
  9. Open Source Mathematical Software (opinion piece) with David Joyner, November 2007. The link is in the upper right corner of the site.
  10. The Birch and Swinnerton-Dyer Conjecture, a Computational Approach, (70 pages), 2007, free online book.
  11. Explicit Heegner points: Kolyvagin's conjecture and non-trivial elements in the Shafarevich-Tate group, with Dimitar Jetchev and Kristin Lauter (18 pages), 2007, accepted.
  12. Modular Forms: A Computational Approach (free online book) or buy it from the AMS or buy it from Amazon.com; with an appendix by Paul Gunnells (282 pages), AMS Graduate Studies in Mathematics, Vol. 79.
  13. Average Ranks of Elliptic Curves, with Baur Bektemirov, Barry Mazur and Mark Watkins (19 pages), 2007, appeared in the Bulletins of the AMS.
  14. The Manin Constant, with Amod Agashe and Ken Ribet (22 pages), 2006, accepted.
  15. Verification of the Birch and Swinnerton-Dyer Conjecture for Specific Elliptic Curves, with G. Grigorov, A. Jorza, S. Patrikis, and C. Patrascu (26 pages)
    , 2005
  16. Computation of p-Adic Heights and Log Convergence, with Barry Mazur and John Tate (36 pages), 2005, appeared.
  17. Visualizing Elements of Shafarevich-Tate Groups at Higher Level, with Dimitar Jetchev (28 pages), 2007, to appear in Documenta Mathematica
  18. Visibility of Mordell-Weil Groups (20 pages), 2007, to appear in Documenta Mathematica
  19. A Brief Introduction To Classical and Adelic Algebraic Number Theory (190 pages), free online book.
  20. Conjectures About Discriminants of Hecke Algebras of Prime Level, with Frank Calegari (ANTS VI Proceedings, 2004).
  21. Modular Degrees of Neumann-Setzer Curves, with Mark Watkins (IMRN 2004, no 27, 1395-1405).
  22. Studying the Birch and Swinnerton-Dyer Conjecture for Modular Abelian Varieties Using MAGMA (appeared as a chapter in a book for Springer-Verlag edited by John Cannon).
  23. A Database of Elliptic Curves---First Report, with Mark Watkins (ANTS V proceedings, Sydney, Australia, 2002).
  24. Constructing Elements in Shafarevich-Tate Groups of Modular Motives, with Neil Dummigan and Mark Watkins ("Number theory and algebraic geometry--to Peter Swinnerton-Dyer on his 75th birthday", Ed. M. Reid and A. Skorobogatov, pages 91-118).
  25. Shafarevich-Tate Groups of Nonsquare Order (Progress in Math., 224 (2004), 277-289, Birkhauser).
  26. Approximation of Infinite-Slope Modular Eigenforms By Finite-Slope Eigenforms, with Robert Coleman (Dwork Proceedings).
  27. J1(p) Has Connected Fibers, with Brian Conrad and Bas Edixhoven (Documenta Mathematica, 8 (2003), pages 331-408).
  28. Visible Evidence for the Birch and Swinnerton-Dyer Conjecture for Rank 0 Modular Abelian Varieties, with Amod Agashe, and an appendix by Mazur and Cremona (in Math. Comp., Vol 74, Number 249, pages 455-484).
  29. Visibility of Shafarevich-Tate Groups of Abelian Varieties, with Amod Agashe (J. of Number Theory, 97 (2002), no. 1, 171-185.)
  30. Component Groups of Purely Toric Quotients of Semistable Jacobians, with Brian Conrad (Math. Res. Letters, 8 (2001) no. 5-6, 745-766)
  31. Appendix on Generating the Hecke Algebra, with Amod Agashe (Experimental Math., 11 (2002), no. 2, 303-311).
  32. The field generated by the points of small prime order on an elliptic curve, with Loic Merel (IMRN, 2001, no. 20, 1075-1082.)
  33. An introduction to computing modular forms using modular symbols (to appear in an MSRI proceedings).
  34. Lectures on Serre's conjectures, with Ken Ribet (Arithmetic Algebraic Geometry, IAS/Park City Math. Inst. Series, Vol. 9, 143-232).
  35. Cuspidal modular symbols are transportable, with Helena Verrill (LMS Journal of Computation and Mathematics, 4 (2001), 170-181).
  36. There are genus one curves over Q of every odd index (J. Reine Angew. Math. 547 (2002), 139-147).
  37. A mod five approach to modularity of icosahedral Galois representations, with Kevin Buzzard (Pac. J. Math. 203 (2002), no. 2, 265-282)
  38. Explicit approaches to modular abelian varieties (UC Berkeley Ph.D. thesis)
  39. Component groups of quotients of J0(N), with David Kohel (ANTS IV proceedings)
  40. Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves, with five coauthors (Mathematics of Computation, 70 (2001), no . 236, 1675-1697).