Asymptotic density and the asymptotics of partition functions

2000/02/13 by Melvyn B. Nathanson, Nathanson, Melvyn B.
Mathematics · #11B05 #11P70 #11P82 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT #msc:11B05 #msc:11P70 #msc:11P82

paper · pdf · doi:10.48550/arxiv.math/0002103

17 pages. To appear in Acta Math. Hungarica

arxiv created 2000/02/13 · arxiv updated 2009/11/30

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 = π√(2/3). Let α> 0. It is proved that log p_A(n) ~ c√(αn) if and only if the set A has asymptotic density α.

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