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Millennial Conference on Number Theory
May 21-26, 2000
University of Illinois
Urbana, IL, USA

Organizers
B.C. Berndt, N. Boston, H.G. Diamond, A.J. Hildebrand, W. Philipp

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

We address the optimality of Ramanaujan's famous congruences for the partition function modulo powers of 5. Are there subprogressions of Ramanujan's arithmetic progressions, other than those found by Ramanujan himself, where the congruence modulo 5j is in fact a congruence modulo a higher power of 5? This question is answered affirmatively by explicitly exhibiting infinitely many distinct systematic extensions of Ramanujan's congruences modulo 5j to congruences modulo 5j + 1.

Date received: March 1, 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 # cadx-42.