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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm102-2-3,
author = {Wolfgang A. Schmid},
title = {On the asymptotic behavior of some counting functions, II},
journal = {Colloquium Mathematicae},
volume = {103},
year = {2005},
pages = {197-216},
zbl = {1143.11351},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm102-2-3}
}
Wolfgang A. Schmid. On the asymptotic behavior of some counting functions, II. Colloquium Mathematicae, Tome 103 (2005) pp. 197-216. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm102-2-3/