Arithmetic and Analysis of the Series Σn=1∞ 1/n sin x/n

被引：0

作者：

Sebbar, Ahmed ^{[1
,2
]}

Gay, Roger ^{[2
]}

机构：

[1] Chapman Univ, One Univ Dr, Orange, CA 92866 USA

[2] Univ Bordeaux, UMR 5251, IMB, F-33405 Talence, France

来源：

COMPLEX ANALYSIS AND OPERATOR THEORY | 2021年 / 15卷 / 03期

关键词：

Hardy-Littlewood function; Franel integral; Beurling's theorem; Arithmetic functions;

D O I：

10.1007/s11785-021-01097-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we connect a celebrated theorem of Nyman and Beurling on the equivalence between the Riemann hypothesis and the density of some functional space in L-2(0,1) to a trigonometric series considered first by Hardy and Littlewood (see (3.4)). We highlight some of its curious analytical and arithmetical properties.

引用

页数：29

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