Partial sums of the cotangent function

被引：0

作者：

Bettin, Sandro ^{[1
]}

Drappeau, Sary ^{[2
]}

机构：

[1] DIMA Dipartimento Matemat, Via Dodecaneso 35, I-16146 Genoa, Italy

[2] Aix Marseille Univ, CNRS, Cent Marseille, UMR I2M 7373, F-13453 Marseille, France

来源：

JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX | 2020年 / 32卷 / 01期

关键词：

Cotangent sum; continued fraction;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove the existence of reciprocity formulae for sums of the form Sigma(k-1)(m=1) f (m/k) cot (pi mh/k) where f is a piecewise C-1 function, featuring an alternating phenomenon not visible in the classical case where f (x) = x. We deduce bounds for these sums in terms of the continued fraction expansion of h/k.

引用

页码：217 / 230

页数：14

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