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

Wolfgang A. Schmid. "Periods of sets of lengths: a quantitative result and an associated inverse problem." Colloquium Mathematicae 113.1 (2008): 33-53. <http://eudml.org/doc/284298>.

@article{WolfgangA2008,
abstract = {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.},
author = {Wolfgang A. Schmid},
journal = {Colloquium Mathematicae},
keywords = {almost arithmetical multiprogression; block monoid; factorization length; number field},
language = {eng},
number = {1},
pages = {33-53},
title = {Periods of sets of lengths: a quantitative result and an associated inverse problem},
url = {http://eudml.org/doc/284298},
volume = {113},
year = {2008},
}

TY - JOUR
AU - Wolfgang A. Schmid
TI - Periods of sets of lengths: a quantitative result and an associated inverse problem
JO - Colloquium Mathematicae
PY - 2008
VL - 113
IS - 1
SP - 33
EP - 53
AB - 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.
LA - eng
KW - almost arithmetical multiprogression; block monoid; factorization length; number field
UR - http://eudml.org/doc/284298
ER -