Wednesday, October 12
Milner 317, 12:30 PM
Title: An exposition of "Hecke Operators on Gamma_0(m)" by Atkin and Lehner
Abstract: In this talk, we'll be discussing the very important and beautiful paper of Atkin and Lehner in which they describe the action of the Hecke operators on Gamma_0(m) (including the ones dividing the level, which coincide with the "U-operators"). The main results of the paper describe certain subspaces of cusp forms that have basis of simultaneous eigenforms of every operator in sight (including T_p, U_q and the "Atkin-Lehner" operators). Certain striking properties of the coefficients of such eigenforms are described. The background assumed for the talk will be little beyond the definition of modular and cusp forms.