On the average number of cyclic subgroups of the groups \(\mathbb Z_{n_1} \times\mathbb Z_{n_2}\times \mathbb Z_{n_3}\) with \(n_1,n_2,n_3\le x\)

DOI10.1007/s40993-020-0186-6zbMath1452.11116OpenAlexW3003753219MaRDI QIDQ2292256

László Tóth, Zhai, Wenguang

Publication date: 3 February 2020

Published in: Research in Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40993-020-0186-6

zbMATH Keywords

asymptotic formulacyclic groupnumber of cyclic subgroupsfinite abelian group of rank three

Mathematics Subject Classification ID

Asymptotic results on counting functions for algebraic and topological structures (11N45)

Related Items (2)

The cotype zeta function of \(\mathbb{Z}^d\) ⋮ Mean values of multivariable multiplicative functions and applications to the average number of cyclic subgroups and multivariable averages associated with the LCM function

Cites Work

• Unnamed Item
• Multiple zeta functions and asymptotic structure of free Abelian groups of finite rank.
• A new method of proving some classical theorems of Abelian groups.
• A zero-density theorem for the Riemann zeta-function
• Representing and counting the subgroups of the group \(\mathbb{Z}_m \times \mathbb{Z}_n\)
• The cotype zeta function of \(\mathbb{Z}^d\)
• Counting Subgroups in a Direct Product of Finite Cyclic Groups
• An arithmetic method of counting the subgroups of a finite abelian group
• Zeta function of subgroups of abelian groups and average orders
• 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 number of cyclic subgroups of a finite abelian group
• Subgroups of Finite Abelian Groups Having Rank Two via Goursat’s Lemma
• ON THE AVERAGE NUMBER OF SUBGROUPS OF THE GROUP ℤ_m × ℤ_n

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