Výsledky vyhledávání - "Goudout, Élie"

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Th\'eor\`eme d'Erd\H{o}s-Kac pour les translat\'es d'entiers ayant $k$ facteurs premiers

Autor: Goudout, Élie

Publikováno v: J. Number Theory, 210(2020):280-291

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 e

Externí odkaz: http://arxiv.org/abs/1812.04893

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Concentration simultan\'ee de fonctions additives

Autor: Goudout, Élie

Publikováno v: J. Th\'eor. Nombres Bordeaux, 31(2)(2019):385-402

We study the simultaneous concentration of the values of several additive functions along polynomial shifts. Under a slight restriction, this yields an extension of a result from Hal\'asz in 1975.
Comment: 18 pages, in French

Externí odkaz: http://arxiv.org/abs/1809.06599

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Highest perfect power of a product of integers less than $x$

Autor: Goudout, Élie

Publikováno v: Int. J. Number Theory, 14(7)(2018):2043-2044

For $x\geq 3$, we define $w(x)$ as the highest integer $w$ for which there exist integers $m, y\geq 1$ and $1\leq n_1<\dotsC

Externí odkaz: http://arxiv.org/abs/1801.08731

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Lois locales de la fonction $\omega$ dans presque tous les petits intervalles

Autor: Goudout, Élie

Publikováno v: Proc. London Math. Soc. (3), 115(3)(2017):599-637

For $k\geq 1$ an integer and $x\geq 1$ a real number, let $\pi_k(x)$ be the number of integers smaller than $x$ having exactly $k$ distinct prime divisors. Building on recent work of Matom\"aki and Radziwi\l\l, we investigate the asymptotic behavior

Externí odkaz: http://arxiv.org/abs/1607.08666

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

Autor: Goudout, Élie

Publikováno v: Acta Arith., 182(2)(2018):101-116

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)^

Externí odkaz: http://arxiv.org/abs/1603.05809

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