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Article Dans Une Revue Indagationes Mathematicae Année : 2020

The saddle-point method for general partition functions

Résumé

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.

Dates et versions

hal-02921589 , version 1 (25-08-2020)

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Gregory Debruyne, Gérald Tenenbaum. The saddle-point method for general partition functions. Indagationes Mathematicae, 2020, 31 (4), pp.728-738. ⟨10.1016/j.indag.2020.06.010⟩. ⟨hal-02921589⟩
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