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Talk: A modular supercongruence for 6F5: An Apéry-like story

A modular supercongruence for 6F5: An Apéry-like story

Date: 2017/09/17
Occasion: Palmetto Number Theory Series (PANTS XXVIII)
Place: University of Tennessee

Abstract

We discuss congruences between truncated hypergeometric series and modular forms. Specifically, we discuss a supercongruence modulo \(p^3\) between the \(p\)th Fourier coefficient of a weight 6 modular form and a truncated \(_6F_5\)-hypergeometric series. The story is intimately tied with Apéry's proof of the irrationality of \(\zeta(3)\).

This is joint work with Robert Osburn and Wadim Zudilin.

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