PARTITION VALUES AND CENTRAL CRITICAL VALUES OF CERTAIN MODULAR L-FUNCTIONS

Let p(n) denote the number of partitions of a positive number n, let l is an element of {5, 7, 11} and let delta(l) be the least non-negative residue of 24(-1) modulo e. In this paper we prove congruences modulo l between p(ln + delta(l))/l 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 <= l <= 31.