Monomials of Eisenstein series

被引：4

作者：

Griffin, Trevor ^{[1
]}

Kenshur, Nathan ^{[2
]}

Price, Abigail ^{[3
]}

Vandenberg-Daves, Bradshaw ^{[4
]}

Xue, Hui ^{[5
]}

Zhu, Daozhou ^{[5
]}

机构：

[1] Univ Idaho, Moscow, ID 83844 USA

[2] Univ Calif Berkeley, Berkeley, CA 94720 USA

[3] Hillsdale Coll, Hillsdale, MI 49242 USA

[4] Vassar Coll, Poughkeepsie, NY 12604 USA

[5] Clemson Univ, Sch Math & Stat Sci, Clemson, SC 29634 USA

来源：

JOURNAL OF NUMBER THEORY | 2021年 / 219卷

基金：

美国国家科学基金会;

关键词：

Eisenstein series; Zeros; Special values of L-functions; ZEROS;

D O I：

10.1016/j.jnt.2020.09.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let E-k(z) be the normalized Eisenstein series of weight k for the modular group SL(2, Z). We study the zeros of E-k to prove that the equation Pi(n)(i=1) E-ki = Pi(m)(j=1) E-lj has no solutions, except for those given by known relationships between E-4, E-6, E-8, E-10, and E-14. We go on to discuss some implications of this result. (c) 2020 Elsevier Inc. All rights reserved.

引用

页码：445 / 459

页数：15

共 12 条

[1]

Batut C., 1998, User's Guide to PARI-GP Universite Bordeaux

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