On the asymptotic behavior of some counting functions

Maciej Radziejewski, and Wolfgang A. Schmid. "On the asymptotic behavior of some counting functions." Colloquium Mathematicae 102.2 (2005): 181-195. <http://eudml.org/doc/283448>.

@article{MaciejRadziejewski2005,
abstract = {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.},
author = {Maciej Radziejewski, Wolfgang A. Schmid},
journal = {Colloquium Mathematicae},
keywords = {factorizations of distinct lengths; zero-sum sequence; block monoid; half-factorial},
language = {eng},
number = {2},
pages = {181-195},
title = {On the asymptotic behavior of some counting functions},
url = {http://eudml.org/doc/283448},
volume = {102},
year = {2005},
}

TY - JOUR
AU - Maciej Radziejewski
AU - Wolfgang A. Schmid
TI - On the asymptotic behavior of some counting functions
JO - Colloquium Mathematicae
PY - 2005
VL - 102
IS - 2
SP - 181
EP - 195
AB - 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.
LA - eng
KW - factorizations of distinct lengths; zero-sum sequence; block monoid; half-factorial
UR - http://eudml.org/doc/283448
ER -