Identities for trigonometric divisor sums

被引：0
|
作者：
Kim, Sun [1 ]
机构：
[1] Univ Illinois, Dept Math, 1409 West Green St, Urbana, IL 61801 USA
来源：
INTERNATIONAL JOURNAL OF NUMBER THEORY | 2017年 / 13卷 / 04期
关键词：
Trigonometric sums; Bessel functions; weighted divisor sums; circle problem; divisor problem; Ramanujan's lost notebook; APPROXIMATE FUNCTIONAL-EQUATION; BESSEL-FUNCTION SERIES; DIOPHANTINE APPROXIMATION;
D O I：
10.1142/S1793042117500506
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The goal of this paper is to prove several identities for sums of the type Sigma(n <= x)'d(n) cos(2 pi na/q), Sigma(n <= x)'nd(n) sin (2 pi na/q), Sigma(n <= x)'r(2)(n)cos (2 pi na/q), where d(n) is the number of divisors of n and r(2)(n) is the number of representations of n as a sum of two squares. Some of our identities involve weighted divisor functions, and most of our identities are new.
引用
收藏
页码：957 / 975
页数：19
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