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

 

Partition values and central critical values of certain modular $ L$-functions


Author: John J. Webb
Journal: Proc. Amer. Math. Soc. 138 (2010), 1263-1272
MSC (2010): Primary 11F33; Secondary 11F11
Published electronically: December 8, 2009
MathSciNet review: 2578520
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Abstract: Let $ p(n)$ denote the number of partitions of a positive number $ n$, let $ \ell \in \{5,7,11\}$ and let $ \delta_\ell$ be the least non-negative residue of $ 24^{-1}$ modulo $ \ell$. In this paper we prove congruences modulo $ \ell$ between $ \frac{p(\ell n+ \delta_\ell)}{\ell}$ and ratios of central critical values of $ L$-functions associated to twists of certain integer weight newforms. In 1999, Guo and Ono proved analogous results for $ 13\leq \ell \leq 31$.


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Additional Information

John J. Webb
Affiliation: Department of Mathematics, University of South Carolina, Columbia, South Caro- lina 29208
Email: webbjj3@mailbox.sc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10188-0
PII: S 0002-9939(09)10188-0
Received by editor(s): August 28, 2009
Published electronically: December 8, 2009
Communicated by: Ken Ono
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.