Sur l'inégalité de Turán-Kubilius friable

Sur l'inégalité de Turán-Kubilius friable

An integer n is said to be y-friable if its largest prime factor P (n) does not exceed y. By convention, P (1) := 1. Classical notations are S(x, y) := {n x : P (n) y} for the set of y-friable integers not exceeding x and Ψ(x, y) for its cardinality. The study of friable restrictions of arithmetic functions is closely connected to the Kubilius model of probabilistic number theory. In this frame...

Inégalité de Turán-Kubilius friable et indépendance asymptotique

Elaborating on previous works and taking advantage of estimates on the local behaviour of the counting function of friable integers, we determine the optimal range in which the friable Turán-Kubilius constant tends to 1.

Constantes de Turán-Kubilius friables: une étude numérique

method, saddle-point method. This study is a follow-up to two recent works: [la Bretèche et Tenenbaum 05] and [Martin et Tenenbaum 08]. The former provides a friable (i.e., with respect to integers free of large prime factors) extension of the classical Turán–Kubilius inequality, while the latter furnishes a theoretical method for sharp evaluation of the involved constants. Here, we complement ...

Etat actuel de nos connaissances sur les argasidés de l'Iran

Sur la frequence de leptospirose en Iran