Mean values of multivariable multiplicative functions and applications to the average number of cyclic subgroups and multivariable averages associated with the LCM function

DOI10.1016/j.jnt.2021.07.027zbMath1492.11139arXiv2108.10247OpenAlexW3193850849WikidataQ114156775 ScholiaQ114156775MaRDI QIDQ2116764

Christoper Salinas Zavala, László Tóth, Driss Essouabri

Publication date: 18 March 2022

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

Full work available at URL: https://arxiv.org/abs/2108.10247

zbMATH Keywords

meromorphic continuationmultiplicative functionsTauberian theoremszeta functionsLCM multivariable averagesmean values of multivariable arithmetic functionssubgroups averages

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Other Dirichlet series and zeta functions (11M41) Multiple Dirichlet series and zeta functions and multizeta values (11M32) Tauberian theorems (11M45)

Related Items (3)

Additive arithmetic functions meet the inclusion-exclusion principle: asymptotic formulas concerning the GCD and LCM of several integers ⋮ On the reciprocal sum of lcm of \(k\)-tuples ⋮ The cotype zeta function of \(\mathbb{Z}^d\)

Cites Work

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• On mean values of multivariable complex valued multiplicative functions and applications
• 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 \(n_1,n_2,n_3\le x\)
• Height zeta functions on generalized projective toric varieties
• 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
• On certain sums concerning the gcd’s and lcm’s of k positive integers
• ON THE AVERAGE NUMBER OF SUBGROUPS OF THE GROUP ℤ_m × ℤ_n

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