Arithmetic of coefficients of half-integral weight modular forms
by
Scott Ahlgren
University of Illinois
Coauthors: Matthew Boylan

We study the distribution of coefficients of half-integral weight modular forms modulo prime powers. In particular we obtain conditions which guarantee that these coefficients are "well distributed'' in residue classes. As an application we resolve many cases of an old conjecture of M. Newman on the distribution of the ordinary partition p(n).

Date received: May 1, 2004