Periods of sets of lengths: a quantitative result and an associated inverse problem
Colloquium Mathematicum, Tome 113 (2008) no. 1, pp. 33-53
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $\mathcal{P}(H,\mathcal{D}, M)(x)$, counting elements whose sets of lengths have period $\mathcal{D}$, for extreme choices of $\mathcal{D}$. 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.
Keywords:
investigation quantitative aspects non unique factorizations ring integers algebraic number field gives rise combinatorial problems class group number field paper investigate combinatorial problems related function mathcal mathcal counting elements whose sets lengths have period mathcal extreme choices mathcal class group meets certain conditions obtain value exponent asymptotic formula function results imply oscillations error term
Affiliations des auteurs :
Wolfgang A. Schmid 1
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title = {Periods of sets of lengths: a quantitative result and an associated inverse problem},
journal = {Colloquium Mathematicum},
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year = {2008},
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Wolfgang A. Schmid. Periods of sets of lengths: a quantitative result and an associated inverse problem. Colloquium Mathematicum, Tome 113 (2008) no. 1, pp. 33-53. doi: 10.4064/cm113-1-4
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