On a supercongruence conjecture of Rodriguez-Villegas

Abstract

In examining the relationship between the number of points overFp\mathbb {F}_pon certain Calabi-Yau manifolds and hypergeometric series which correspond to a particular period of the manifold, Rodriguez-Villegas identified numerically 22 possible supercongruences. We prove one of the outstanding supercongruence conjectures between a special value of a truncated generalized hypergeometric series and thepp-th Fourier coefficient of a modular form.