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Théorème d'Erdős-Kac pour les translatés d'entiers ayant $k$ facteurs premiers
Published 12 Dec 2018 in math.NT | (1812.04893v1)
Abstract: Let $x\geqslant 3$. For $1\leqslant n\leqslant x$ an integer, let $\omega(n)$ be its number of distinct prime factors. We show that $\omega(n-1)$ satisfies an Erd\H{o}s-Kac type theorem whenever $\omega(n)=k$ where $1\leqslant k\ll\log\log x$, thus extending a result of Halberstam.
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