On the zeros of period functions associated to the Eisenstein series for Γ0+ (N)

被引：0

作者：

Choi, SoYoung ^{[1
]}

Im, Bo-Hae ^{[2
]}

机构：

[1] Gyeongsang Natl Univ, Dept Math Educ, RINS, 501 Jinjudae-ro,, Jinju 52828, South Korea

[2] Korea Adv Inst Sci & Technol, Dept Math Sci, 291 Daehak-ro, Daejeon 34141, South Korea

来源：

JOURNAL OF NUMBER THEORY | 2022年 / 234卷

基金：

新加坡国家研究基金会;

关键词：

Period functions; Eisenstein series; N-self-inversive polynomials; SELF-INVERSIVE POLYNOMIALS;

D O I：

10.1016/j.jnt.2021.06.021

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the period functions associated to the Eisenstein series for the Fricke group Gamma(+)(0) (N), the odd parts of the period functions and certain polynomials obtained from the period functions for Gamma(+)(0) (N), and we prove that all zeros of each of them lie on the circle |z| = 1/root N by applying the properties of a self-inversive polynomial. In particular, our result proves Berndt and Straub's suggested problem. (c) 2021 Elsevier Inc. All rights reserved.

引用

页码：200 / 239

页数：40

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