September 26, 2003

Handouts:
- This is a much-improved new version of the handout from last time: moduli_and_ramification.pdf
- These are the slides for a powerpoint presentation on modular symbols: PDF, handout, Powerpoint
- This is a paper I wrote for an MSRI conference/ is an introduction to computing with modular forms using modular symbols: PDF
I recommend that you look at Manin's paper Parabolic points and zeta functions of modular curves over the weekend. I hope to talk about it on Monday.
You can download MAGMA for your PC from this site.
Discuss the Weil pairing, and how it is important in understanding what X(N) parametrizes.
Discuss ramification of X(N) over X(1).
State the ramification degrees over 0, 1728, and oo, and use them to deduce the genus formula for X(N).
Show the powerpoint presentation on modular symbols (see above handout).
I will not have office hours today.