On a supercongruence conjecture of Rodriguez-Villegas

McCarthy, Dermot

doi:10.1090/S0002-9939-2011-11087-6

On a supercongruence conjecture of Rodriguez-Villegas
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by Dermot McCarthy PDF

Proc. Amer. Math. Soc. 140 (2012), 2241-2254 Request permission

Abstract:

In examining the relationship between the number of points over $\mathbb {F}_p$ on 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 the $p$-th Fourier coefficient of a modular form.

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