Coefficients of half-integral weight modular forms modulo ℓj

Scott David Ahlgren, Matthew Boylan

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)219-239
Number of pages21
JournalMathematische Annalen
Volume331
Issue number1
DOIs
StatePublished - Jan 2005

ASJC Scopus subject areas

  • Mathematics(all)

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