A Reciprocity Formula for a Cotangent Sum

被引：34

作者：

Bettin, Sandro ^{[1
]}

Conrey, John Brian ^{[1
,2
]}

机构：

[1] Univ Bristol, Bristol, Avon, England

[2] Amer Inst Math, Palo Alto, CA USA

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2013年 / 2013卷 / 24期

基金：

美国国家科学基金会;

关键词：

RIEMANN ZETA-FUNCTION; PERIOD FUNCTIONS; NYMAN;

D O I：

10.1093/imrn/rns211

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce the cotangent sum c(h/k)=-Sigma(k-1)(a=1) a/k cot pi ah/k and prove that it satisfies hc(h/k) + c(k/h) - 1/pi k = g(h/k), where g is a function which is analytic on the complex plane minus the negative real axis. The sum arises in connection with the Nyman-Beurling approach to the Riemann hypothesis.

引用

页码：5709 / 5726

页数：18

共 11 条

[1]

Báez-Duarte L, 2005, RAMANUJAN J, V9, P215, DOI 10.1007/s11139-005-0834-4

[2] On Nyman, Beurling and Baez-Duarte's Hilbert space reformulation of the Riemann hypothesis [J].