Weighted divisor sums and Bessel function series, IV

被引：10

作者：

Berndt, Bruce C. ^{[2
]}

Kim, Sun ^{[1
]}

Zaharescu, Alexandru ^{[2
,3
]}

机构：

[1] Ohio State Univ, Dept Math, Columbus, OH 43210 USA

[2] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[3] Acad Romana, Inst Math, Bucharest 70700, Romania

来源：

RAMANUJAN JOURNAL | 2012年 / 29卷 / 1-3期

关键词：

Circle problem; Bessel functions; Riesz sums; Weighted divisor sums; Dirichlet L-series; Ramanujan's Lost Notebook; IDENTITIES;

D O I：

10.1007/s11139-011-9352-8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

One fragment (p. 335) published with Ramanujan's Lost Notebook contains two formulas, each involving a finite trigonometric sum and a doubly infinite series of Bessel functions. The identities are connected with the classical circle and divisor problems, respectively. This paper is devoted to the first identity. First, we obtain a generalization in the setting of Riesz sums. Second, we prove a trigonometric analogue.

引用

页码：79 / 102

页数：24

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