Mathematische Annalen

, Volume 331, Issue 1, pp 219–239

Coefficients of half-integral weight modular forms modulo ℓj

Article

DOI: 10.1007/s00208-004-0555-9

Cite this article as:
Ahlgren, S. & Boylan, M. Math. Ann. (2005) 331: 219. doi:10.1007/s00208-004-0555-9

Abstract.

Suppose that ℓ≥5 is prime, that j≥0 is an integer, and that F(z) is a half-integral weight modular form with integral Fourier coefficients. We give some general conditions under which the coefficients of F are “well-distributed” modulo ℓj. As a consequence, we settle many cases of a classical conjecture of Newman by proving, for each prime power ℓj with ℓ≥5, that the ordinary partition function p(n) takes each value modulo ℓj infinitely often.

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IllinoisUrbanaUSA