Thursday, April 8
Milner 216, 1:00 PM
Title: Gaussian hypergeometric functions and traces of Hecke operators
Abstract: We will express traces of Hecke operators on spaces of newforms in terms of values of hypergeometric functions over finite fields. With specfic examples in mind (from levels 2, 4, & 8), we will consider simplifications of the Eichler-Selberg trace formula in terms of counting points on varieties over finite fields. Then ultimately we will reformulate these traces in terms of hypergeometric functions which are constructed from Gauss and Jacobi sums. Joint work with K. Ono and M. Papanikolas.