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Bibliographic Details
Main Authors: Sui, Yankun, Liu, Dan, Zhou, Boling
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2504.00331
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Table of Contents:
  • Let ${\Bbb Z}_{m}$ be the additive group of residue classes modulo $m$ and $s(m_{1},m_{2})$ denote the number of subgroups of the group ${\Bbb Z}_{m_{1}}\times {\Bbb Z}_{m_{2}}$, where $m_{1}$ and $m_{2}$ are arbitrary positive integers. We consider sums of type $\sum\limits_{\substack{m_{1}m_{2}\leq x \\ m_{1}m_{2}\in N_{k}}}s(m_{1},m_{2})$, where $N_{k}$ is the set of $k$-th power of natural numbers. In particular, we deduce asymptotic formulas with $k=2$ and $k=3$.