On the error term concerning the number of subgroups of the groups \(\mathbb{Z}_m \times \mathbb{Z}_n\) with \(mn \leq x\)

DOI10.1016/J.JNT.2020.03.001zbMath1455.11130OpenAlexW3021094081MaRDI QIDQ784721

Dan Liu, Yankun Sui

Publication date: 3 August 2020

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2020.03.001

zbMATH Keywords

asymptotic formulaDirichlet seriesexponential sumerror termmean squarePerron formulanumber of cyclic subgroupsnumber of subgroups

Mathematics Subject Classification ID

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

Related Items (4)

On the weighted average number of subgroups of ℤm × ℤn with mn ≤ x ⋮ Hyperbolic summation for functions of the GCD and LCM of several integers ⋮ Error term concerning number of subgroups of group \(\mathbb{Z}_m \times \mathbb{Z}_n\) with \(m^2 + n^2 \le x\) ⋮ On certain sums of arithmetic functions involving the GCD and LCM of two positive integers

Cites Work

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• Recent progress on the Dirichlet divisor problem and the mean square of the Riemann zeta-function
• On estimations of trigonometric sums over primes in short intervals. III
• A zero-density theorem for the Riemann zeta-function
• Many-Dimensional Generalized Divisor Problems
• 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 AVERAGE NUMBER OF SUBGROUPS OF THE GROUP ℤ_m × ℤ_n

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