Fang-Ting Tu

Louisiana State University Louisiana State University

A Whipple Formula Revisited

Heilbronn Number Theory Seminar

28th April 2021, 4:00 pm – 5:00 pm

This talk is based on 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 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. In this talk, I will use an example to demonstrate our approach and relate the hypergeometric values to certain periods of modular forms.

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