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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

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
Published electronically: November 7, 2011
MathSciNet review: 2898688
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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 $ p$-th Fourier coefficient of a modular form.


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Additional Information

Dermot McCarthy
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
Email: mccarthy@math.tamu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-11087-6
Received by editor(s): November 10, 2010
Received by editor(s) in revised form: February 18, 2011
Published electronically: November 7, 2011
Additional Notes: This work was supported by the UCD Ad Astra Research Scholarship program.
Communicated by: Kathrin Bringmann
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.



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