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On a supercongruence conjecture of Rodriguez-Villegas

Author: Dermot McCarthy
Journal: Proc. Amer. Math. Soc. 140 (2012), 2241-2254
MSC (2010): Primary 11F33; Secondary 33C20, 11T24
Posted: November 7, 2011
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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 -th Fourier coefficient of a modular form.

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