Title: On asymptotic behavior of Dirichlet inverse
Authors: Baustian, Falko
Bobkov, Vladimír
Citation: BAUSTIAN, F., BOBKOV, V. On asymptotic behavior of Dirichlet inverse. International Journal of Number Theory, 2020, roč. 16, č. 6, s. 1337-1354. ISSN 1793-0421.
Issue Date: 2020
Publisher: World Scientific Publishing
Document type: článek
URI: 2-s2.0-85082101878
ISSN: 1793-0421
Keywords in different language: Dirichlet inverse;Dirichlet convolution;asymptotics;ordered factorizations
Abstract in different language: Let f(n) be an arithmetic function with f(1)≠0 and let f−1(n) be its reciprocal with respect to the Dirichlet convolution. We study the asymptotic behavior of ∣∣f−1(n)∣∣ with regard to the asymptotic behavior of |f(n)| assuming that the latter one grows or decays with at most polynomial or exponential speed. As a by-product, we obtain simple but constructive upper bounds for the number of ordered factorizations of n into k factors.
Rights: © World Scientific Publishing
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