On a supercongruence conjecture of Rodriguez-Villegas

Details On a supercongruence conjecture of Rodriguez-Villegas On a supercongruence conjecture of Rodriguez-Villegas

2012-04-06

arxiv.org/abs/1204.1575v1

Proc. Amer. Math. Soc. \textbf{140} (2012), 2241--2254

Mathematics

Number Theory

Scientific paper

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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