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

 

A formula and a congruence for Ramanujan's $\tau$-function


Author: Matthew Papanikolas
Journal: Proc. Amer. Math. Soc. 134 (2006), 333-341
MSC (2000): Primary 11F30; Secondary 11F33, 11T24, 33C99
Published electronically: June 14, 2005
MathSciNet review: 2175999
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Abstract: We determine formulas for Ramanujan's $\tau$-function and for the coefficients of modular forms on $\Gamma_0(2)$ in terms of finite field ${}_3F_2$-hypergeometric functions. Using these formulas we obtain a new congruence of $\tau(p) \pmod{11}$.


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Additional Information

Matthew Papanikolas
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
Email: map@math.tamu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08029-9
PII: S 0002-9939(05)08029-9
Received by editor(s): April 27, 2004
Received by editor(s) in revised form: September 9, 2004
Published electronically: June 14, 2005
Additional Notes: This research was supported by NSF grant DMS-0340812 and NSA grant MDA904-03-1-0019
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.