2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58680Let 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\sqrt(2/3). Let α> 0. It is proved that log p_A(n) ~ c\sqrt(αn) if and only if the set A has asymptotic density α.17 pages. To appear in Acta Math. HungaricaNumber TheoryCombinatorics11P82,11P70,11B05text