Rationality of the Petersson Inner Product of Cohen's Kernels

被引：0

作者：

You, Yuanyi ^{[1
]}

Zhang, Yichao ^{[1
,2
]}

机构：

[1] Harbin Inst Technol, Sch Math, Harbin 150001, Peoples R China

[2] Harbin Inst Technol, Inst Adv Study Math HIT, Harbin 150001, Peoples R China

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2022年 / 18卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Cohen's kernel; rationality; double Eisenstein series; Fourier coefficient;

D O I：

10.1142/S1793042122500749

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

By explicitly calculating and then analytically continuing the Fourier expansion of the twisted double Eisenstein series E-s,E-k-s*(z, w; 1/2) of Diamantis and O'Sullivan, we prove a formula of the Petersson inner product. of Cohen's kernel and one of its twists, and obtain a rationality result. This extends a result of Kohnen and Zagier.

引用

页码：1445 / 1463

页数：19

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