Asymptotic density and the asymptotics of partition functions

Details Asymptotic density and the asymptotics of partition functions Asymptotic density and the asymptotics of partition functions

2000-02-13

arxiv.org/abs/math/0002103v1

Mathematics

Number Theory

17 pages. To appear in Acta Math. Hungarica

Scientific paper

Let A be a set of positive integers with gcd(A) = 1, and let p_A(n) be the
partition function of A. Let c = \pi \sqrt(2/3). Let \alpha > 0. It is proved
that log p_A(n) ~ c\sqrt(\alpha n) if and only if the set A has asymptotic
density \alpha.

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