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On the asymptotic behavior of some counting functions. II. (English) Zbl 1143.11351
Summary: 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.
Part I, cf. Colloq. Math. 102, No. 2, 181–195 (2005; Zbl 1143.11346).

##### MSC:
 11R27 Units and factorization 05C35 Extremal problems in graph theory 11R47 Other analytic theory 20K01 Finite abelian groups
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