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 -