PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

Théorème d’Erdős–Kac dans presque tous les petits intervalles

Volume 182 / 2018

Élie Goudout Acta Arithmetica 182 (2018), 101-116 MSC: Primary 11N25. DOI: 10.4064/aa8480-11-2017 Published online: 11 January 2018


We show that the Erdős–Kac theorem is valid in almost all intervals $[x,x+h]$ as $h$ tends to infinity with $x$. We also show that for all $k$ near $\log\log x$, almost all intervals $[x,x+\exp((\log\log x)^{1/2+\varepsilon})]$ contain the expected number of integers $n$ such that $\omega(n)=k$. These results are a consequence of the methods introduced by Matomäki and Radziwiłł to estimate sums of multiplicative functions over short intervals.


  • Élie GoudoutÉcole Normale Supérieure
    45 rue d’Ulm
    75230 Paris Cedex 05, France
    Institut de Mathématiques de Jussieu-PRG
    Université Paris Diderot, Sorbonne Paris Cité
    75013 Paris, France

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image