Event Type:

Number Theory Seminar

Date/Time:

Tuesday, January 18, 2022 - 10:00 to 10:50

Location:

TBA

Guest Speaker:

Institution:

Louisiana State University

Abstract:

In this talk, I will give an introduction to hypergeometric functions over finite fields and some recent developments including joint work (https://arxiv.org/pdf/2103.08858.pdf) with Wen-Ching Winnie Li and Ling Long. In this joint project, we consider the hypergeometric data corresponding to a formula due to Whipple which relates certain hypergeometric values _7F_6(1) and _4F_3(1). When the hypergeometric data are primitive and defined over the rationals, from identities of hypergeometric character sums, we explain a special structure of the corresponding Galois representations behind Whipple's formula leading to a decomposition that can be described by the Fourier coefficients of Hecke eigenforms. I will use an example to demonstrate our approach and relate the hypergeometric values to certain periods of modular forms.

Host: