Geodesic
On the asymptotic behavior of some counting functions, II
Wolfgang A. Schmid1
1 Institute for Mathematics and Scientific Computing Karl-Franzens-Universität Heinrichstrasse 36 8010 Graz, Austria
Colloquium Mathematicum, Tome 102 (2005) no. 2, pp. 197-216.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The investigation of the counting function of the set of integral elements, in an algebraic number field, with factorizations of at most $k$ different lengths gives rise to a combinatorial constant depending only on the class group of the number field and the integer $k$. In this paper the value of these constants, in case the class group is an elementary $p$-group, is estimated, and determined under additional conditions. In particular, it is proved that for elementary $2$-groups these constants are equivalent to constants that are investigated in extremal graph theory.
DOI : 10.4064/cm102-2-3
Keywords: investigation counting function set integral elements algebraic number field factorizations different lengths gives rise combinatorial constant depending only class group number field integer paper value these constants class group elementary p group estimated determined under additional conditions particular proved elementary groups these constants equivalent constants investigated extremal graph theory

Wolfgang A. Schmid 1

1 Institute for Mathematics and Scientific Computing Karl-Franzens-Universität Heinrichstrasse 36 8010 Graz, Austria 
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Wolfgang A. Schmid. On the asymptotic behavior of some counting functions, II. Colloquium Mathematicum, Tome 102 (2005) no. 2, pp. 197-216. doi : 10.4064/cm102-2-3. http://geodesic.mathdoc.fr/articles/10.4064/cm102-2-3/

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