On a sum involving the divisor function

被引：17

作者：

Ma, Jing ^{[1
]}

Sun, Huayan ^{[1
]}

机构：

[1] Jilin Univ, Sch Math, Changchun 130012, Peoples R China

来源：

PERIODICA MATHEMATICA HUNGARICA | 2021年 / 83卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Divisor function; Asymptotic formula; Exponent pair;

D O I：

10.1007/s10998-020-00378-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let d(n) be the divisor function and denote by [t] the integral part of the real number t. In this short note, we prove that Sigma(n <= x) d([x/n]) = x Sigma(m >= 1) d(m)/m(m+1) + O-epsilon(x(11/23+epsilon)) for x -> infinity.

引用

页码：185 / 191

页数：7

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