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

John J. Webb
2010 Proceedings of the American Mathematical Society  
Let p(n) denote the number of partitions of a positive number n, let ∈ {5, 7, 11} and let δ be the least non-negative residue of 24 −1 modulo . In this paper we prove congruences modulo between p( n+δ ) 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 ≤ ≤ 31.
doi:10.1090/s0002-9939-09-10188-0 fatcat:jlozeqxb4few7courb4hqkoh7e