On the asymptotic behavior of some counting functions

• Autorzy: Maciej Radziejewski , Wolfgang A. Schmid
• Języki publikacji: EN

Abstrakty

EN

The investigation of certain counting functions of elements with given factorization properties in the ring of integers of an algebraic number field gives rise to combinatorial problems in the class group. In this paper a constant arising from the investigation of the number of algebraic integers with factorizations of at most k different lengths is investigated. It is shown that this constant is positive if k is greater than 1 and that it is also positive if k equals 1 and the class group satisfies some additional conditions. These results imply that the corresponding counting function oscillates about its main term. Moreover, some new results on half-factorial sets are obtained.

Kategorie tematyczne

• 11R27: Units and factorization
• 20K01: Finite abelian groups [For sumsets, see and ]
• 11N64: Other results on the distribution of values or the characterization of arithmetic functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2005
• Tom: 102
• Numer: 2
• Strony: 181-195

Daty

wydano

2005

Twórcy

autor

Maciej Radziejewski

• Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland

autor

Wolfgang A. Schmid

• Institute for Mathematics and Scientific Computing, Karl-Franzens-Universität, Heinrichstrasse 36, 8010 Graz, Austria

Identyfikatory

DOI

10.4064/cm102-2-2