The saddle-point method for general partition functions
Combinatorics
2022-05-27 v4 Number Theory
Abstract
We apply the saddle-point method to derive asymptotic estimates or asymptotic series for the number of partitions of a natural integer into parts chosen from a subset of the positive integers whose associated Dirichlet series satisfies certain analytic properties. This enables grouping in a single statement many cases studied in the literature, as well as a number of new ones.
Keywords
Cite
@article{arxiv.2004.05227,
title = {The saddle-point method for general partition functions},
author = {Gregory Debruyne and Gérald Tenenbaum},
journal= {arXiv preprint arXiv:2004.05227},
year = {2022}
}
Comments
A few minor corrections with respect to the journal version are added in this version. In particular we corrected the application of the Phragm\'en-Lindel\"of principle on p.3 which required a minor adaptation of the properties (d) and (f)