Arithmetical semigroups. III: Elements with prime factors in residue classes
type: Item
instance of: scholarly article
title: Arithmetical semigroups. III: Elements with prime factors in residue classes
zbMATH Open document ID: 0827.11057
DOI: 10.1007/BF01293674
author: Richard Warlimont
published in: Monatshefte für Mathematik
publication date: 1995-04-09T00:00:00Z
full work available at URL: https://eudml.org/doc/178683
review text: The author studies an arithmetical semigroup \((G, \partial)\) satisfying Axiom \(A^\#\) as defined and stated in the reviewer's monograph [Analytic arithmetic of algebraic function fields, M. Dekker (1979; Zbl 0411.10001)]. The asymptotic distribution of elements of \(G\) is investigated subject to the condition that the degrees \(\partial (p)\) of the prime elements \(p\) of the canonical prime decompositions all lie in a given union of integer residue classes modulo a fixed integer \(k\). The results obtained are analogous to those for the classical similar problem concerning natural numbers, derived in Section 183 of \textit{E. Landau} [Handbuch der Lehre von der Verteilung der Primzahlen, Chelsea (1953; Zbl 0051.280)]. Nevertheless the analogy is not trivial, involving different types of formulae and analytical techniques. [Further parts of this series have been reviewed in (I) Zbl 0723.11048, (II) Zbl 0735.11046, (IV) Zbl 0809.11058, (V) Zbl 0809.11059].
Mathematics Subject Classification ID: 11N80
Mathematics Subject Classification ID: 11N45
Mathematics Subject Classification ID: 11N25
zbMATH DE Number: 742705
zbMATH Keywords: arithmetical semigroup
zbMATH Keywords: asymptotic distribution of elements
zbMATH Keywords: prime elements
zbMATH Keywords: residue classes
reviewed by: John Knopfmacher
MaRDI profile type: Publication
cites work: Arithmetical semigroups. I: Direct factors
cites work: Q4198823
cites work: Q5820649
cites work: Das asymptotische Verhalten von Summen über multiplikative Funktionen
description: scientific article; zbMATH DE number 742705