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Une étude asymptotique probabiliste des coefficients d'une série entière
Abstract : Following the ideas of Rosenbloom [7] and Hayman [5], Luis B ́aez-Duarte gives in [1] a probabi- listic 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 B ́aez-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 (Erd ̈os-Lehner [4], Ingham [6]).
Keywords :
number theory
probability theory
Cited literature [7 references]
https://hal.univ-cotedazur.fr/hal-00720010
Contributor : Michel Miniconi <>
Submitted on : Wednesday, July 24, 2013 - 4:11:45 PM
Last modification on : Tuesday, May 26, 2020 - 6:50:08 PM
Document(s) archivé(s) le : Wednesday, April 5, 2017 - 4:26:01 PM
Contributor : Michel Miniconi <>
Submitted on : Wednesday, July 24, 2013 - 4:11:45 PM
Last modification on : Tuesday, May 26, 2020 - 6:50:08 PM
Document(s) archivé(s) le : Wednesday, April 5, 2017 - 4:26:01 PM
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