Asymptotic density and the asymptotics of partition functions
Melvyn B. Nathanson
Abstract
Let A be a set of positive integers with gcd(A) = 1, and let pA(n) be the partition function of A. Let c = π(2/3). Let α> 0. It is proved that log pA(n) ~ c(αn) if and only if the set A has asymptotic density α.
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