On the error term concerning the number of subgroups of the groups $\mathbb {Z}_m \times \mathbb {Z}_n$ with $m,n\le x$

DOI10.4064/aa171111-7-2zbMath1435.11130OpenAlexW2808067907MaRDI QIDQ4581941

László Tóth, Zhai, Wenguang

Publication date: 21 August 2018

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/aa171111-7-2

zbMATH Keywords

asymptotic formulaDirichlet serieserror termcyclic groupPerron formulanumber of cyclic subgroupsnumber of subgroupsfinite abelian group of rank two

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Finite abelian groups (20K01) Arithmetic functions; related numbers; inversion formulas (11A25) Subgroups of abelian groups (20K27)

Related Items (9)

Counting subrings of the ring $\Bbb{Z}_m \times \Bbb{Z}_n$ ⋮ On the reciprocal sum of lcm of \(k\)-tuples ⋮ On the average number of subgroups of the group \(\mathbb{Z}_m \times \mathbb{Z}_n\) with \(k\)-th power sequence ⋮ On the weighted average number of subgroups of ℤm × ℤn with mn ≤ x ⋮ Error term concerning number of subgroups of group \(\mathbb{Z}_m \times \mathbb{Z}_n\) with \(m^2 + n^2 \le x\) ⋮ Manin's conjecture for a class of singular cubic hypersurfaces ⋮ 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 \(n_1,n_2,n_3\le x\) ⋮ On the error term concerning the number of subgroups of the groups \(\mathbb{Z}_m \times \mathbb{Z}_n\) with \(mn \leq x\) ⋮ 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
• A new method of proving some classical theorems of Abelian groups.
• An arithmetic method of counting the subgroups of a finite abelian group
• Exponential Sums and Lattice Points III
• ON THE AVERAGE NUMBER OF SUBGROUPS OF THE GROUP ℤ_m × ℤ_n

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