Supercongruence Conjectures of Rodriguez-villegas
نویسنده
چکیده
Abstract. In examining the relationship between the number of points over Fp on certain Calabi-Yau manifolds and hypergeometric series which correspond to a particular period of the manifold, Rodriguez-Villegas identified 22 possible supercongruences. We provide a framework of congruences covering all 22 cases. Using this framework we prove one of the outstanding supercongruence conjectures between a special value of a truncated ordinary hypergeometric series and the p-th Fourier coefficient of a modular form. In the course of this work we also establish two new binomial coefficient-harmonic sum identities.
منابع مشابه
On a Supercongruence Conjecture of Rodriguez-villegas
In examining the relationship between the number of points over Fp 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-...
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