On Fourier coefficients of modular forms of half integral weight at squarefree integers

被引：2

作者：

Jiang, Y. -J. ^{[1
]}

Lau, Y. -K. ^{[2
]}

Lue, G. -S. ^{[3
]}

Royer, E. ^{[4
]}

Wu, J. ^{[5
]}

机构：

[1] Shandong Univ, Sch Math & Stat, Weihai 264209, Shandong, Peoples R China

[2] Univ Hong Kong, Dept Math, Pokfulam Rd, Hong Kong, Peoples R China

[3] Shandong Univ, Dept Math, Jinan 250100, Shandong, Peoples R China

[4] Univ Clermont Auvergne, CNRS, LMBP, F-63000 Clermont Ferrand, France

[5] Univ Paris Est Creteil, CNRS, LAMA 8050, Lab Anal & Math Appl, F-94010 Creteil, France

来源：

MATHEMATISCHE ZEITSCHRIFT | 2019年 / 293卷 / 1-2期

基金：

中国博士后科学基金;

关键词：

Fourier coefficients; Half-integral weight modular forms; Dirichlet series; SIGN;

D O I：

10.1007/s00209-018-2191-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the Dirichlet series associated to the Fourier coefficients of a half-integral weight Hecke eigenform at squarefree integers extends analytically to a holomorphic function in the half-plane Res>12. This exhibits a high fluctuation of the coefficients at squarefree integers and improves a sign-change result in Lau et al. (Mathematika 62:866-883, 2016).

引用

页码：789 / 808

页数：20

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