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1 JAD - Laboratoire Jean Alexandre Dieudonné

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





Autor: Bernard Candelpergher - Michel Miniconi -

Fuente: https://hal.archives-ouvertes.fr/



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