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Bernard Candelpergher; Michel Miniconi
Une étude asymptotique probabiliste des coefficients d’une série entière
(A probabilistic asymptotic study of the coefficients of a power series)
Journal de théorie des nombres de Bordeaux, 26 no. 1 (2014), p. 45-67, doi: 10.5802/jtnb.858
Article PDF | Reviews MR 3232766 | Zbl 1296.60054

Résumé - 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]).

Bibliography

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