On the distribution of prime divisors in arithmetical semigroups
type: Item
instance of: scholarly article
title: On the distribution of prime divisors in arithmetical semigroups
zbMATH Open document ID: 0964.11036
author: Anna Iwaszkiewicz-Rudoszańska
published in: Functiones et Approximatio. Commentarii Mathematici
publication date: 2001-07-19T00:00:00Z
review text: The analytic theory of arithmetical semigroups was developed by \textit{A. Geroldinger} and \textit{J. Kaczorowski} [Sémin. Théorie Nombres Bordx. 4, 199-238 (1992; Zbl 0780.11046)]. An arithmetical semigroup \(S\) is said to be of type \(\beta\) if \(L(1,\chi)=0\) holds for a certain nontrivial character \(\chi\) of the associated class group of \(S\). In the note under review the author shows among other results that for a given arbitrary finite abelian group \(G\) of even order there exist infinitely many arithmetical semigroups \(S\) of type \(\beta\) with class group \(G\) and with in some sense prescribed distribution of the generators of \(S\).
reviewed by: Helmut Müller
Mathematics Subject Classification ID: 11M41
Mathematics Subject Classification ID: 20M14
zbMATH DE Number: 1442082
zbMATH Keywords: arithmetical semigroups
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1442082