On a generalisation of Bordelles-Dai-Heyman-Pan-Shparlinski's conjecture

JOURNAL OF NUMBER THEORY

卷:236

Article

Ma, J.¹  Wu, J.²  Zhao, F.³ 

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

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

[3] North China Univ Water Resources & Elect Power, Dept Math & Informat Sci, Jinshui E Rd, Zhengzhou 450046, Henan, Peoples R China

关键词: Euler totient function;    Integral part;    Exponential sums;    Exponent pair;   

DOI  :  10.1016/j.jnt.2021.07.024

来源: Elsevier

【 摘 要 】

Let f be an arithmetic function satisfying some simple conditions. The aim of this paper is to establish an asymptotical formula for the quantity & nbsp;S-f(x) :=& nbsp; sigma(n zeta x)& nbsp;f([x/n])& nbsp;for x -> infinity, where [t] is the integral part of the real number t. This generalises some recent results of Bordelles, Dai, Heyman, Pan & Shparlinski and of Zhai (f = phi = the Euler function), and of Zhao & Wu (f = sigma = the sum-of-divisors function). (C)& nbsp;2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free