On a supercongruence conjecture of Rodriguez-Villegas

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Abstract

In examining the relationship between the number of points over 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.

Original languageEnglish
Pages (from-to)2241-2254
Number of pages14
JournalProceedings of the American Mathematical Society
Volume140
Issue number7
DOIs
StatePublished - 2012

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