ON SIGN CHANGES OF PRIMITIVE FOURIER COEFFICIENTS OF SIEGEL CUSP FORMS

被引：0

作者：

Shankhadhar, Karam Deo ^{[1
]}

Tiwari, Prashant ^{[2
]}

机构：

[1] Indian Inst Sci Educ & Res Bhopal, Dept Math, Bhopal Bypass Rd, Bhopal 462066, Madhya Pradesh, India

[2] Harish Chandra Res Inst, Chhatnag Rd, Allahabad 211019, Uttar Pradesh, India

来源：

FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI | 2023年 / 68卷 / 02期

关键词：

Siegel modular forms; Jacobi forms; primitive Fourier coefficients; sign changes; MODULAR-FORMS;

D O I：

10.7169/facm/2101

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish quantitative results for sign changes in certain subsequences of primitive Fourier coefficients of a non-zero Siegel cusp form of arbitrary degree over congruence subgroups. As a corollary of our result for degree two Siegel cusp forms, we get sign changes of its diagonal Fourier coefficients. In the course of our proofs, we prove the non-vanishing of certain type of Fourier-Jacobi coefficients of a Siegel cusp form and all theta components of certain Jacobi cusp forms of arbitrary degree over congruence subgroups, which are also of independent interest.

引用

页码：257 / 274

页数：18

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