Cotangent sums, quantum modular forms, and the generalized Riemann hypothesis

被引：8

作者：

Lewis, John ^{[1
]}

Zagier, Don ^{[2
]}

机构：

[1] MIT, 77 Massachusetts Ave, Cambridge, MA 02139 USA

[2] Max Planck Inst Math, Bonn, Germany

来源：

RESEARCH IN THE MATHEMATICAL SCIENCES | 2019年 / 6卷 / 01期

关键词：

PERIOD FUNCTIONS;

D O I：

10.1007/s40687-018-0159-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that an asymptotic property of the determinants of certain matrices whose entries are finite sums of cotangents with rational arguments is equivalent to the GRH for odd Dirichlet characters. This is then connected to the existence of certain quantum modular forms related to Maass Eisenstein series.

引用

页数：24

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