Columbia Mathematics Department Colloquium


On the parity of coefficients of modular forms


Joël Bellaïche

Brandeis University



Recently Nicolas and Serre have determined the structure of the Hecke
algebra acting on modular forms of level 1 modulo 2, and Serre has
conjectured the existence of a universal Galois representation over
this algebra. I'll explain the proof of this conjecture, and show how
that representation may be used to get new information on the parity
of the coefficients of  modular forms of level 1
-- for example, on the parity of the values of the generalized Ramanujan's tau
functions. I'll also explain a still conjectural relation with the
partition function.


Wednesday, November 28th, 5:00 - 6:00 p.m.
Mathematics 520
Tea will be served at 4:30 p.m.