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arXiv · 1307.6435

Une étude asymptotique probabiliste des coefficients d'une série entière

Bernard Candelpergher·Michel Miniconi
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Abstract

Following the ideas of Rosenbloom [7] and Hayman [5], Luis Báez-Duarte gives in [1] a probabilistic proof of Hardy-Ramanujan's asymptotic formula for the partitions of an integer. The main principle of the method relies on the convergence in law of a family of random variables to a gaussian variable. In our work we prove a theorem of the Liapounov type (Chung [2]) that justifies this convergence. To obtain simple asymptotic formulæ a condition of the so-called strong Gaussian type defined by Luis Báez-Duarte is required; we demonstrate this in a situation that make it possible to obtain a classical asymptotic formula for the partitions of an integer with distinct parts (Erdös-Lehner [4], Ingham [6]).

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Bernard Candelpergher, Michel Miniconi. 2013-07-24. Une étude asymptotique probabiliste des coefficients d'une série entière. https://arxiv.org/abs/1307.6435

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