Théorème d'Erdős-Kac pour les translatés d'entiers ayant $k$ facteurs premiers

Abstract

Let $x⩾3$. For $1⩽n⩽x$ an integer, let $\omega (n)$ be its number of distinct prime factors. We show that $\omega (n-1)$ satisfies an Erdős-Kac type theorem whenever $\omega (n)=k$ where $1⩽k\ll \log \log x$, thus extending a result of Halberstam.

9 pages, in French