2013/07/24 by Bernard Candelpergher, Candelpergher, Bernard, Michel Miniconi +1
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #Probability (math.PR) #math.NT #math.PR
paper · pdf · doi:10.48550/arxiv.1307.6435
19 pages, texte en français
arxiv created 2013/07/24 · arxiv updated 2013/07/25
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]).