On the Vanishing of the Coefficients of CM Eta Quotients

被引：2

作者：

Huber, Tim ^{[1
]}

Liu, Chang ^{[2
]}

McLaughlin, James ^{[3
]}

Ye, Dongxi ^{[2
]}

Yuan, Miaodan ^{[2
]}

Zhang, Sumeng ^{[2
]}

机构：

[1] Univ Texas Rio Grande Valley, Sch Math & Stat Sci, Edinburg, TX 78539 USA

[2] Sun Yat Sen Univ, Sch Math Zhuhai, Zhuhai, Guangdong, Peoples R China

[3] West Chester Univ, Math Dept, W Chester, PA USA

来源：

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY | 2023年 / 66卷 / 04期

关键词：

CM eta quotients; Fourier coefficients; vanishingness; MODULAR-FORMS;

D O I：

10.1017/S0013091523000627

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This work characterizes the vanishing of the Fourier coefficients of all CM (Complex Multiplication) eta quotients. As consequences, we recover Serre's characterization about that of n(12z)(2 )and recent results of Chang on the pth coefficients of n(4z)(6 ) and n(6z)(4). Moreover, we generalize the results on the cases of weight 1 to the setting of binary quadratic forms.

引用

页码：1202 / 1216

页数：15

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