Mean values of multivariable multiplicative functions and applications to the average number of cyclic subgroups and multivariable averages associated with the LCM function

JOURNAL OF NUMBER THEORY

卷:236

Article

Essouabri, Driss¹  Zavala, Christoper Salinas¹  Toth, Laszlo² 

[1] Univ Jean Monnet St Etienne, Inst Camille Jordan, Fac Sci & Tech, UMR CNRS 5208, 23 Rue Doc Paul Michelon, F-42023 Saint Etienne, France

[2] Univ Pecs, Dept Math, Ifjusag Utja 6, H-7624 Pecs, Hungary

关键词: Mean values of multivariable;    arithmetic functions;    Multiplicative functions;    Zeta functions;    Meromorphic continuation;    Tauberian theorems;   

DOI  :  10.1016/j.jnt.2021.07.027

来源: Elsevier

【 摘 要 】

We use multiple zeta functions to prove, under suitable assumptions, precise asymptotic formulas for the averages of multivariable multiplicative functions. As applications, we prove some conjectures on the average number of cyclic subgroups of the group Z(m1) x center dot center dot center dot & nbsp;x Z(mn) and multivariable averages associated with the LCM function. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free