On Erdos's elementary method in the asymptotic theory of partitions
Number Theory
2007-05-23 v1 Combinatorics
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) ~ \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).
Cite
@article{arxiv.math/0002171,
title = {On Erdos's elementary method in the asymptotic theory of partitions},
author = {Melvyn B. Nathanson},
journal= {arXiv preprint arXiv:math/0002171},
year = {2007}
}
Comments
14 pages. To appear in the proceedings of the conference "Paul Erdos and his Mathematics," which was held in Budapest in July,1999