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

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