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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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