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.

中文翻译：

---

一般配分函数的鞍点法

我们应用鞍点方法来推导将自然整数分割成部分的渐近估计或渐近级数，这些部分是从正整数的子集中选择的，这些部分的相关狄利克雷级数满足某些解析性质。这使得可以将文献中研究的许多案例以及许多新案例组合在一个语句中。