Weighted Divisor Sums and Bessel Function Series

被引：0

作者：

Bruce C. Berndt

Alexandru Zaharescu

机构：

[1] University of Illinois,Department of Mathematics

[2] Institute of Mathematics of the Romanian Academy,undefined

来源：

Mathematische Annalen | 2006年 / 335卷

关键词：

Positive Integer; Bessel Function; Lost; Infinite Series; Summatory Function;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

On page 335 in his lost notebook, Ramanujan records without proof an identity involving a finite trigonometric sum and a doubly infinite series of ordinary Bessel functions. We provide the first published proof of this result. The identity yields as corollaries representations of weighted divisor sums, in particular, the summatory function for r2(n), the number of representations of the positive integer n as a sum of two squares.

引用

页码：249 / 283

页数：34

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