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