On asymptotic behavior of Dirichlet inverse-Reference-Cited by-同舟云学术

On asymptotic behavior of Dirichlet inverse

Published:2020-02-25 Issue:06 Volume:16 Page:1337-1354
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

Baustian Falko¹,Bobkov Vladimir²³

Affiliation:

1. Department of Mathematics, University of Rostock, Ulmenstraße 69, Rostock 18057, Germany

2. Department of Mathematics and NTIS, Faculty of Applied Sciences, University of West Bohemia, Univerzitní 8, Plzeň 301 00, Czech Republic

3. Institute of Mathematics, Ufa Federal Research Centre, RAS, Chernyshevsky str. 112, Ufa 450008, Russia

Abstract

Let [Formula: see text] be an arithmetic function with [Formula: see text] and let [Formula: see text] be its reciprocal with respect to the Dirichlet convolution. We study the asymptotic behavior of [Formula: see text] with regard to the asymptotic behavior of [Formula: see text] 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 [Formula: see text] into [Formula: see text] factors.

Funder

Agency of the Czech Republic and Czech Ministry of Education, Youth and Sports

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042120500700

Reference22 articles.

1. Modular Functions and Dirichlet Series in Number Theory

2. Basis properties of eigenfunctions of the 𝑝-Laplacian

3. On the number of ordered factorizations of natural numbers

4. Constructive Bounds on Ordered Factorizations

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