TY - JOUR

T1 - On a supercongruence conjecture of Rodriguez-Villegas

AU - McCarthy, Dermot

PY - 2012/7

Y1 - 2012/7

N2 - 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.

AB - 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.

U2 - 10.1090/S0002-9939-2011-11087-6

DO - 10.1090/S0002-9939-2011-11087-6

M3 - Article

SP - 2241

EP - 2254

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

ER -