Modular Forms, Fall 2009, L. Washington
Time: Tuesdays, Thursdays 9:30am-10:45am
Room: Math 0411
Text: Modular Forms: A classical and computational introduction} by L. J. P. Kilford
The course will roughly follow Kilford's book, with amplification of some of the topics.
Main topics:
Modular forms for SL2(Z)
Congruence subgroups
Eisenstein series
Fundamental domains and modular curves
Finite-dimensionality results
Hecke operators
Newforms
Mod p modular forms
Galois representations
Applications (elliptic curves, Fermat's Last Theorem, representations by quadratic forms, ...)
Homework #1 (due September 21)
page 38: 3, 11, 14, 18, 19.
For problem 3: show that it's incorrect, then fix it and prove the correct version.
Homework #2 (due October 20):
pdf file