arXiv Analytics

Sign in

arXiv:math/0002103 [math.NT]AbstractReferencesReviewsResources

Asymptotic density and the asymptotics of partition functions

Melvyn B. Nathanson

Published 2000-02-13Version 1

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.

Comments: 17 pages. To appear in Acta Math. Hungarica
Categories: math.NT, math.CO
Subjects: 11P82, 11P70, 11B05
Related articles: Most relevant | Search more
arXiv:1809.07584 [math.NT] (Published 2018-09-20)
Additive Complements for a given Asymptotic Density
arXiv:2209.07887 [math.NT] (Published 2022-09-16)
Error bounds for the asymptotic expansion of the partition function
arXiv:2412.02257 [math.NT] (Published 2024-12-03)
Asymptotics for the reciprocal and shifted quotient of the partition function

Links

Toolbox