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Supercongruences between truncated $_{2}F_{1}$ hypergeometric functions and their Gaussian analogs

Author: Eric Mortenson
Journal: Trans. Amer. Math. Soc. 355 (2003), 987-1007
MSC (2000): Primary 11F85, 11L10
Published electronically: October 25, 2002
MathSciNet review: 1938742
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Abstract: Fernando Rodriguez-Villegas has conjectured a number of supercongruences for hypergeometric Calabi-Yau manifolds of dimension $d\le 3$. For manifolds of dimension $d=1$, he observed four potential supercongruences. Later the author proved one of the four. Motivated by Rodriguez-Villegas's work, in the present paper we prove a general result on supercongruences between values of truncated $_{2}F_{1}$hypergeometric functions and Gaussian hypergeometric functions. As a corollary to that result, we prove the three remaining supercongruences.

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Additional Information

Eric Mortenson
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706

Keywords: Supercongruences
Received by editor(s): February 27, 2002
Received by editor(s) in revised form: July 22, 2002
Published electronically: October 25, 2002
Article copyright: © Copyright 2002 American Mathematical Society

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