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On Erdos's elementary method in the asymptotic theory of partitions

Melvyn B. Nathanson
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Abstract

Let m be a positive integer, and let A be the set of all positive integers that belong to a union of r distinct congruence classes modulo m. We assume that the elements of A are relatively prime, that is, gcd(A) = 1. Let p_A(n) denote the number of partitions of n into parts belonging to A. We obtain the asymptotic formula log p_A(n) ~ π\sqrt(2rn/3m). The proof is based on Erdos's elementary method to obtain the asymptotic formula for the usual partition function p(n).

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Melvyn B. Nathanson. 2000-02-21. On Erdos's elementary method in the asymptotic theory of partitions. https://arxiv.org/abs/math/0002171

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