Th\'eor\`eme d'Erd\H{o}s-Kac dans presque tous les petits intervalles
| Autor: | Goudout, Élie |
|---|---|
| Jazyk: | francouzština |
| Rok vydání: | 2016 |
| Předmět: | |
| Zdroj: | Acta Arith., 182(2)(2018):101-116 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.4064/aa8480-11-2017 |
| Popis: | 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. Comment: 16 pages, in French. Corrected typos, added e-mail address |
| Databáze: | arXiv |
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