Summation of values of multiplicative functions on semigroups
type: Item
instance of: scholarly article
title: Summation of values of multiplicative functions on semigroups
zbMATH Open document ID: 0840.11040
DOI: 10.1007/BF00970942
published in: Lithuanian Mathematical Journal
publication date: 1995-09-18T00:00:00Z
review text: Let \(G\) be an arithmetic semigroup with the norm function written additively and satisfying the Axiom \(A^\sharp\) in the notation used by \textit{J. Knopfmacher} [Analytic arithmetic of algebraic function fields (Dekker 1979; Zbl 0411.10001)]. In the paper, a mean value theorem of the Wirsing-Delange-Halász type with a remainder for a class of multiplicative functions defined on \(G\) is proved. Using this result and in a natural way modified notion of the discrepancy over \(G\) a big O and Omega estimation for the discrepancy of the set \(\xi\omega(a)\), where \(\xi\) stands for an irrational number and \(\omega(a)\) for the number of distinct prime divisors of an element \(a\in G\), is proved.
Mathematics Subject Classification ID: 11N80
Mathematics Subject Classification ID: 11N37
Mathematics Subject Classification ID: 11K06
zbMATH DE Number: 794493
zbMATH Keywords: arithmetic semigroup
zbMATH Keywords: mean value theorem
zbMATH Keywords: multiplicative functions
zbMATH Keywords: discrepancy
author: Eugenijus Manstavičius
author: R. Skrabutenas
reviewed by: Štefan Porubský
MaRDI profile type: Publication
cites work: Q4870689
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full work available at URL: https://doi.org/10.1007/bf00970942
OpenAlex ID: W2026278536
description: scientific article; zbMATH DE number 794493