On the interlacing of the zeros of certain Poincare cusp forms

被引：1

作者：

Dhillon, Sonika ^{[1
]}

Kala, Divyanshu ^{[1
]}

Saha, Ekata ^{[1
]}

机构：

[1] Indian Inst Technol Delhi, Dept Math, New Delhi 110016, India

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2023年 / 528卷 / 02期

关键词：

Poincare series; Cusp forms; Location of zeros; Interlacing of zeros; EISENSTEIN SERIES; PROPERTY;

D O I：

10.1016/j.jmaa.2023.127540

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Rankin proved that a specific family of Poincare series (Gk(z, 1))k & GE;24 which are cusp forms have all their finite zeros on the unit circle of the standard fundamental domain F for the action of SL(2, Z) on the complex upper half-plane H. In this article, we show that these finite zeros of Gk(z, 1) and those of Gk+12(z, 1) interlace on fe & iota;& theta; : & theta; & ISIN; (7r/2, 27r/3)}.& COPY; 2023 Elsevier Inc. All rights reserved.

引用

页数：20

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