Partition values and central critical values of certain modular $L$-functions
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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 $13\leq \ell \leq 31$.References
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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
- Received by editor(s): August 28, 2009
- Published electronically: December 8, 2009
- Communicated by: Ken Ono
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 1263-1272
- MSC (2010): Primary 11F33; Secondary 11F11
- DOI: https://doi.org/10.1090/S0002-9939-09-10188-0
- MathSciNet review: 2578520