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arXiv · 1603.05809

Th\'eor\`eme d'Erd\H{o}s-Kac dans presque tous les petits intervalles

Élie Goudout
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Abstract

We show that the Erd\H{o}s-Kac theorem is valid in almost all intervals $\left[x,x+h\right]$ as soon as $h$ tends to infinity with $x$. We also show that for all $k$ near $\log\log x$, almost all interval $\left[x,x+\exp\left(\left(\log\log x\right)^{1/2+\varepsilon}\right)\right]$ contains the expected number of integers $n$ such that $\omega(n)=k$. These results are a consequence of the methods introduced by Matom\"aki and Radziwi\l\l\ to estimate sums of multiplicative functions over short intervals.

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Élie Goudout. 2016-03-18. Th\'eor\`eme d'Erd\H{o}s-Kac dans presque tous les petits intervalles. https://doi.org/10.4064/aa8480-11-2017

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