Contribution à la théorie des entiers friables

Abstract : Call integer y friable if its largest prime factor does not exceed y. We study friable integers in the context of analytic and probabilistic number theory. We first address a problem initiated by Davenport in 1937, and explore conditions of validity for various generalizations of his expansion of the sine function as series of fractional part. These generalizations are described by a pair of functions, satisfaiying the convolution formula f = g * 1. We treat the case when g is the Piltz function of order z [belongs to] C. In a second part, we investigate the asymptotic behaviour of the optimal constant in a friable version of the Turan-Kubilius inequality. Elaborating on recent results of La Bretèche et Tenenbaum, we generalize an asymptotic formula for the variance of an arithmetic additive function established by Hildebrand en 1983.
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Bruno Martin. Contribution à la théorie des entiers friables. Mathématiques générales [math.GM]. Université Henri Poincaré - Nancy 1, 2005. Français. ⟨NNT : 2005NAN10016⟩. ⟨tel-01754418⟩

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