arminstraub.com

# Talk: A modular supercongruence for 6F5: An Apéry-like story (PANTS)

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

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.