In\'egalit\'e de Tur\'an-Kubilius friable et ind\'ependance asymptotique

TL;DR

This paper investigates the asymptotic independence of friable integers using Turán-Kubilius constants, identifying the optimal conditions for their convergence to 1 based on local counting function estimates.

Contribution

It advances understanding of the asymptotic behavior of friable integers by precisely determining the range where the Turán-Kubilius constant approaches 1.

Findings

Identifies the optimal range for the Turán-Kubilius constant to tend to 1

Utilizes estimates on the local behavior of the counting function of friable integers

Enhances previous results with refined asymptotic analysis

Abstract

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 Tur\'an-Kubilius constant tends to $1$.