On a supercongruence conjecture of Rodriguez-Villegas

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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.
Original languageEnglish
Pages (from-to)2241-2254
JournalProceedings of the American Mathematical Society
StatePublished - Jul 2012


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