Coefficients of half-integral weight modular forms

被引：22

作者：

Bruinier, JH ^{[1
]}

Ono, K ^{[1
]}

机构：

[1] Univ Wisconsin, Dept Math, Madison, WI 53706 USA

来源：

JOURNAL OF NUMBER THEORY | 2003年 / 99卷 / 01期

基金：

美国国家科学基金会;

关键词：

half-integral weight modular forms; the partition function; L-series;

D O I：

10.1016/S0022-314X(02)00061-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the distribution of the coefficients a(n) of half-integral weight modular forms modulo odd integers M. As a consequence, we obtain improvements of indivisibility results for the central critical values of quadratic twists of L-functions associated with integral weight newforms established in Ono and Skinner (Fourier coefficients of half-integral weight modular forms modulo l, Ann. of Math. 147 (1998) 453-470). Moreover, we find a simple criterion for proving cases of Newman's conjecture for the partition function. (C) 2002 Elsevier Science (USA). All rights reserved.

引用

页码：164 / 179

页数：16

共 17 条

[1] Distribution of the partition function module composite integers M [J].