On a sum involving the Euler totient function

被引：15

作者：

Wu, J. ^{[1
,2
]}

机构：

[1] Yangtze Normal Univ, Sch Math & Stat, Chongqing 408100, Peoples R China

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

来源：

INDAGATIONES MATHEMATICAE-NEW SERIES | 2019年 / 30卷 / 04期

关键词：

Euler totient function; Exponential sums; Exponent pair;

D O I：

10.1016/j.indag.2019.01.009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this short note, we prove that 4/pi(2)x log x + O(x) <= Sigma(n <= x)phi([x/n]) <= (1/3 + 4/pi(2))x log x + O(x), for x -> infinity, where phi(n) is the Euler totient function and [t] is the integral part of real t. This improves recent results of Bordelles-Heyman-Shparlinski and of Dai-Pan. (C) 2019 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.

引用

页码：536 / 541

页数：6

共 6 条

[1]

Bordelles O., 2018, ARXIV180800188V1MATH

[2] DECOUPLING, EXPONENTIAL SUMS AND THE RIEMANN ZETA FUNCTION [J].