Algebra/Number Theory Seminar

A Whipple Formula Revisited

Fang-Ting Tu (LSU)

Thursday, April 29th, 2021
2:00 PM - 3:00 PM
https://rochester.zoom.us/j/95500122594

This talk is based on a recent joint work with Wen-Ching Winnie Li and Ling Long. 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 $\mathbb Q$, 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. In this talk, I will use an example to demonstrate our approach and relate the hypergeometric values to certain periods of modular forms.

Event contact: c dot d dot haessig at rochester dot edu