On the weighted average number of subgroups of ℤm × ℤn with mn ≤ x-Reference-Cited by-同舟云学术

On the weighted average number of subgroups of ℤm × ℤn with mn ≤ x

Published:2022-04-28 Issue:09 Volume:18 Page:2005-2013
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Kiuchi Isao¹,Saad Eddin Sumaia²^ORCID

Affiliation:

1. Department of Mathematical Sciences, Faculty of Science, Yamaguchi University, Yoshida 1677-1, Yamaguchi 753-8512, Japan

2. Institute of Financial Mathematics and Applied Number Theory, Johannes Kepler University, Altenbergerstrasse 69, 4040 Linz, Austria

Abstract

Let [Formula: see text] be the additive group of residue classes modulo [Formula: see text]. For any positive integers [Formula: see text] and [Formula: see text], let [Formula: see text] and [Formula: see text] denote the total number of subgroups and cyclic subgroups of the group [Formula: see text], respectively. Define [Formula: see text] In this paper, we study the asymptotic behavior of the functions [Formula: see text] and [Formula: see text].

Funder

Austrian Science Fund

Publisher

World Scientific Pub Co Pte Ltd

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042122501020

Reference8 articles.

1. Representing and Counting the Subgroups of the Group Zm×Zn

2. The mean square of the divisor function

3. Cambridge Studies in Advanced Mathematics;Montgomery H. L.,2007

4. ON THE AVERAGE NUMBER OF SUBGROUPS OF THE GROUP ℤm × ℤn

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Counting Subgroups of the Groups $${\mathbb {Z}}_{n_1} \times \cdots \times {\mathbb {Z}}_{n_k}$$: A Survey;Trends in Mathematics;2023-12-28

2. Hyperbolic summation for functions of the GCD and LCM of several integers;The Ramanujan Journal;2022-12-28