On the weighted average number of subgroups of ℤm × ℤn with mn ≤ x
Isao Kiuchi, Sumaia Saad Eddin · International Journal of Number Theory · 2022
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].