Extension of Ramanujan's Congruences for the Partition Function Modulo Powers of 5
by
Jeremy Lovejoy
Pennsylvania State University
Coauthors: Ken Ono (Pennsylvania State University)

We address the optimality of Ramanujan's famous congruences in arithmetic progressions for the partition function modulo powers of 5. Specifically, are there subprogressions, other than those found by Ramanujan himself, where the congruence modulo 5^k is indeed a congruence modulo a higher power of 5? We answer this question in the affirmative by explicitly exhibiting infinitely many distinct systematic extensions from a congruence modulo 5^k to a congruence modulo 5^k+1.

Date received: March 31, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caef-05.