Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 11F85, 11L10

Retrieve articles in all journals with MSC (2000): 11F85, 11L10


Additional Information

Eric Mortenson
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email: mort@math.wisc.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-02-03172-0
PII: S 0002-9947(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