Asymptotic density and the asymptotics of partition functions
Number Theory
2007-05-23 v1 Combinatorics
Abstract
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.
Cite
@article{arxiv.math/0002103,
title = {Asymptotic density and the asymptotics of partition functions},
author = {Melvyn B. Nathanson},
journal= {arXiv preprint arXiv:math/0002103},
year = {2007}
}
Comments
17 pages. To appear in Acta Math. Hungarica