On the distribution of prime divisors in arithmetical semigroups
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 \(S\).
scientific article; zbMATH DE number 1442082
scientific article