On a sum involving the Mangoldt function

被引：23

作者：

Ma, Jing ^{[1
]}

Wu, Jie ^{[2
]}

机构：

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

[2] Univ Paris Est Creteil, CNRS, Lab Anal & Mathemat Appl, LAMA 8050, F-94010 Creteil, France

来源：

PERIODICA MATHEMATICA HUNGARICA | 2021年 / 83卷 / 01期

基金：

中国国家自然科学基金;

关键词：

von Mangoldt function; Asymptotic formula;

D O I：

10.1007/s10998-020-00359-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let Lambda(n) be the von Mangoldt function, and let [t] be the integral part of real number t. In this note we prove that the asymptotic formula (n <= x)Sigma Lambda([x/n]) = x(d >= 1)Sigma Lambda(d)/d(d+1) + O-epsilon((x35/71+epsilon)) holds as x ->infinity for any epsilon > 0.

引用

页码：39 / 48

页数：10

共 6 条

[1] On a sum involving the Euler function [J].

Bordelles, Olivier ;

Dai, Lixia ;

Heyman, Randell ;

Pan, Hao ;

Shparlinski, Igor E. .

JOURNAL OF NUMBER THEORY, 2019, 202 :278-297

[2]

Kolesnik G, 1991, LONDON MATH SOC LECT, P126

[3]

Vaughan R.C., 1980, Acta Arith., V37, P111

[4] Note on a paper by Bordelles, Dai, Heyman, Pan and Shparlinski [J].

Wu, J. .

PERIODICA MATHEMATICA HUNGARICA, 2020, 80 (01) :95-102

[5] On a sum involving the Euler totient function [J].

Wu, J. .

INDAGATIONES MATHEMATICAE-NEW SERIES, 2019, 30 (04) :536-541

[6] On a sum involving the Euler function [J].

Zhai, Wenguang .

JOURNAL OF NUMBER THEORY, 2020, 211 :199-219

← 1 →