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

 

Supercongruences for truncated ${}_{n+1}F_{n}$ hypergeometric series with applications to certain weight three newforms


Author: Eric Mortenson
Journal: Proc. Amer. Math. Soc. 133 (2005), 321-330
MSC (2000): Primary 11F85, 11L10
Published electronically: September 20, 2004
MathSciNet review: 2093051
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Abstract: We prove general results on supercongruences between values of truncated $_{n+1}F_{n}$ hypergeometric functions and their character analogs. As a consequence of the main results of this paper, we prove Beukers-type supercongruences for certain weight three newforms.


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Additional Information

Eric Mortenson
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Address at time of publication: Max-Planck-Institut für Mathematik, Bonn, Germany
Email: mort@mpim-bonn.mpg.de

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07697-X
PII: S 0002-9939(04)07697-X
Keywords: Supercongruences
Received by editor(s): April 16, 2003
Published electronically: September 20, 2004
Communicated by: David E. Rohrlich
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.