TY - JOUR

T1 - Coefficients of half-integral weight modular forms modulo ℓj

AU - Ahlgren, Scott David

AU - Boylan, Matthew

PY - 2005/1

Y1 - 2005/1

N2 - 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.

AB - 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.

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U2 - 10.1007/s00208-004-0555-9

DO - 10.1007/s00208-004-0555-9

M3 - Article

AN - SCOPUS:12144266931

VL - 331

SP - 219

EP - 239

JO - Mathematische Annalen

JF - Mathematische Annalen

SN - 0025-5831

IS - 1

ER -