Abstract

Speaker: Matthew Papanikolas, Texas A&M

Title: Hypergeometric functions over finite fields and coefficients of modular forms

Abstract: Abstract: We consider the problem of determining the Fourier coefficients of modular forms. The Eichler-Selberg trace formula can be used for this purpose, but it is somewhat complicated for practical use. With specific examples in mind (from levels 2, 4, & 8), we will discuss simplifications of the trace formula in terms of counting points on varieties modulo primes and in turn in terms of certain hypergeometric functions over finite fields. Joint work with S. Frechette and K. Ono.