Periods of sets of lengths: a quantitative result and an associated inverse problem

• Autorzy: Wolfgang A. Schmid
• Języki publikacji: EN

Abstrakty

EN

The investigation of quantitative aspects of non-unique factorizations in the ring of integers of an algebraic number field gives rise to combinatorial problems in the class group of this number field. In this paper we investigate the combinatorial problems related to the function 𝓟(H,𝓓,M)(x), counting elements whose sets of lengths have period 𝓓, for extreme choices of 𝓓. If the class group meets certain conditions, we obtain the value of an exponent in the asymptotic formula of this function and results that imply oscillations of an error term.

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: 2008
• Tom: 113
• Numer: 1
• Strony: 33-53

Daty

wydano

2008

Twórcy

autor

Wolfgang A. Schmid

• Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität, Heinrichstraße 36, 8010 Graz, Austria

Identyfikatory

DOI

10.4064/cm113-1-4