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

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

2000-02-21

arxiv.org/abs/math/0002171v1

Mathematics

Number Theory

14 pages. To appear in the proceedings of the conference "Paul Erdos and his Mathematics," which was held in Budapest in July,

Scientific paper

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) ~ \pi \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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