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.
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页数：29
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