Distribution of the partition function modulo composite integers M
by
Scott Ahlgren
Colgate University

Let p(n) denote the usual partition function. Using the theory of modular forms, we prove that if M is a positive integer which is coprime to 6, then there are infinitely many pairs (a, b) of positive integers such that p(an+b)=0 mod M for every non-negative integer n (this extends Ken Ono's results in the case when M is prime). We also make substantial progress towards the resolution of an old conjecture of Newman on the distribution of p(n) modulo M.

Date received: March 9, 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-65.