Supercongruences between truncated hypergeometric functions and their Gaussian analogs

Author:
Eric Mortenson

Journal:
Trans. Amer. Math. Soc. **355** (2003), 987-1007

MSC (2000):
Primary 11F85, 11L10

DOI:
https://doi.org/10.1090/S0002-9947-02-03172-0

Published electronically:
October 25, 2002

MathSciNet review:
1938742

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Abstract | References | Similar Articles | Additional Information

Abstract: Fernando Rodriguez-Villegas has conjectured a number of supercongruences for hypergeometric Calabi-Yau manifolds of dimension . For manifolds of dimension , 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 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

Email:
mort@math.wisc.edu

DOI:
https://doi.org/10.1090/S0002-9947-02-03172-0

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