On the average number of subgroups of the group \(\mathbb{Z}_m \times \mathbb{Z}_n\) with \(k\)-th power sequence

DOI10.1007/S11139-021-00520-WOpenAlexW4206298565MaRDI QIDQ2155879

Dan Liu, Yankun Sui

Publication date: 15 July 2022

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-021-00520-w

zbMATH Keywords

asymptotic formulaDirichlet serieserror termPerron formulanumber of subgroups

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Asymptotic results on counting functions for algebraic and topological structures (11N45) Finite abelian groups (20K01) Subgroups of abelian groups (20K27)

Cites Work

• Recent progress on the Dirichlet divisor problem and the mean square of the Riemann zeta-function
• Representing and counting the subgroups of the group \(\mathbb{Z}_m \times \mathbb{Z}_n\)
• On the error term concerning the number of subgroups of the groups $\mathbb {Z}_m \times \mathbb {Z}_n$ with $m,n\le x$
• ON THE AVERAGE NUMBER OF SUBGROUPS OF THE GROUP ℤ_m × ℤ_n
• Asymptotics for a class of arithmetic functions
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