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

 

Traces of Hecke operators in level 1 and Gaussian hypergeometric functions


Author: Jenny G. Fuselier
Journal: Proc. Amer. Math. Soc. 141 (2013), 1871-1881
MSC (2010): Primary 11F30; Secondary 11T24, 11G20, 33C99
Published electronically: December 10, 2012
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Abstract: We provide formulas for traces of $ p^{th}$ Hecke operators in level 1 in terms of values of finite field $ _2F_1$-hypergeometric functions, extending previous work of the author to all odd primes $ p$ instead of only those $ p \equiv 1 \pmod {12}$. We first give a general level 1 trace formula in terms of the trace of Frobenius on a family of elliptic curves, and then we draw on recent work of Lennon to produce level 1 trace formulas in terms of hypergeometric functions for all primes $ p > 3$.


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Additional Information

Jenny G. Fuselier
Affiliation: Department of Mathematics and Computer Science, High Point University, High Point, North Carolina 27262
Email: jfuselie@highpoint.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11540-0
PII: S 0002-9939(2012)11540-0
Received by editor(s): September 15, 2011
Published electronically: December 10, 2012
Communicated by: Ken Ono
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.