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Journal articles on the topic 'Les entiers friables'

Author: Grafiati
Published: 29 March 2025

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1

Delahaye, Jean-Paul. "Les entiers friables." Pour la Science N° 539 – septembre, no. 9 (September 7, 2022): 80–85. http://dx.doi.org/10.3917/pls.539.0080.

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2

De La Bretèche, Régis, and Gérald Tenenbaum. "Propriétés statistiques des entiers friables." Ramanujan Journal 9, no. 1-2 (March 2005): 139–202. http://dx.doi.org/10.1007/s11139-005-0832-6.

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3

Drappeau, Sary. "Propriétés multiplicatives des entiers friables translatés." Colloquium Mathematicum 137, no. 2 (2014): 149–64. http://dx.doi.org/10.4064/cm137-2-1.

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4

Drappeau, Sary, and Gérald Tenenbaum. "Lois de répartition des diviseurs des entiers friables." Mathematische Zeitschrift 288, no. 3-4 (October 10, 2017): 1299–326. http://dx.doi.org/10.1007/s00209-017-1935-7.

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5

Basquin, Joseph. "Loi de répartition moyenne des diviseurs des entiers friables." Journal de Théorie des Nombres de Bordeaux 26, no. 2 (2014): 281–305. http://dx.doi.org/10.5802/jtnb.868.

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6

Drappeau, Sary. "Théorèmes de type Fouvry–Iwaniec pour les entiers friables." Compositio Mathematica 151, no. 5 (March 3, 2015): 828–62. http://dx.doi.org/10.1112/s0010437x14007933.

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An integer $n$ is said to be $y$-friable if its largest prime factor $P^{+}(n)$ is less than $y$. In this paper, it is shown that the $y$-friable integers less than $x$ have a weak exponent of distribution at least $3/5-{\it\varepsilon}$ when $(\log x)^{c}\leqslant x\leqslant x^{1/c}$ for some $c=c({\it\varepsilon})\geqslant 1$, that is to say, they are well distributed in the residue classes of a fixed integer $a$, on average over moduli ${\leqslant}x^{3/5-{\it\varepsilon}}$ for each fixed $a\neq 0$ and ${\it\varepsilon}>0$. We apply this to the estimation of the sum $\sum _{2\leqslant n\leqslant x,P^{+}(n)\leqslant y}{\it\tau}(n-1)$ when $(\log x)^{c}\leqslant y$. This follows and improves on previous work of Fouvry and Tenenbaum. Our proof combines the dispersion method of Linnik in the setting of Bombieri, Fouvry, Friedlander and Iwaniec with recent work of Harper on friable integers in arithmetic progressions.
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7

de la Bretèche, Régis, and Gérald Tenenbaum. "Une nouvelle approche dans la théorie des entiers friables." Compositio Mathematica 153, no. 3 (February 20, 2017): 453–73. http://dx.doi.org/10.1112/s0010437x16007806.

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Using a new approach starting with a residue computation, we sharpen some of the known estimates for the counting function of friable integers. The improved accuracy turns out to be crucial for various applications, some of which concern fundamental questions in probabilistic number theory.
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8

DE LA BRETÈCHE, R., and D. FIORILLI. "Entiers friables dans des progressions arithmétiques de grand module." Mathematical Proceedings of the Cambridge Philosophical Society 169, no. 1 (March 20, 2019): 75–102. http://dx.doi.org/10.1017/s0305004119000094.

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RésuméWe study the average error term in the usual approximation to the number of y-friable integers congruent to a modulo q, where a ≠ 0 is a fixed integer. We show that in the range exp{(log log x)5/3+ɛ} ⩽ y ⩽ x and on average over q ⩽ x/M with M → ∞ of moderate size, this average error term is asymptotic to −|a| Ψ(x/|a|, y)/2x. Previous results of this sort were obtained by the second author for reasonably dense sequences, however the sequence of y-friable integers studied in the current paper is thin, and required the use of different techniques, which are specific to friable integers.
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9

Hanrot, Guillaume, Gérald Tenenbaum, and Jie Wu. "Moyennes de certaines fonctions multiplicatives sur les entiers friables, 2." Proceedings of the London Mathematical Society 96, no. 1 (September 13, 2007): 107–35. http://dx.doi.org/10.1112/plms/pdm029.

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10

Basquin, Joseph. "Valeurs moyennes de fonctions multiplicatives sur les entiers friables translatés." Acta Arithmetica 145, no. 3 (2010): 285–304. http://dx.doi.org/10.4064/aa145-3-6.

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11

Tenenbaum, Gérald, and Jie Wu. "Moyennes de certaines fonctions multiplicatives sur les entiers friables, 3." Compositio Mathematica 144, no. 2 (March 2008): 339–76. http://dx.doi.org/10.1112/s0010437x07003077.

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AbstractWe consider logarithmic averages, over friable integers, of non-negative multiplicative functions. Under logarithmic, one-sided or two-sided hypotheses, we obtain sharp estimates that improve upon known results in the literature regarding both the quality of the error term and the range of validity. The one-sided hypotheses correspond to classical sieve assumptions. They are applied to provide an effective form of the Johnsen–Selberg prime power sieve.
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12

de la Bret�che, R., and G. Tenenbaum. "Entiers friables : in�galit� de Tur�n?Kubilius et applications." Inventiones mathematicae 159, no. 3 (December 22, 2004): 531–88. http://dx.doi.org/10.1007/s00222-004-0379-y.

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13

Tenenbaum, Gérald. "Sur le biais d’une loi de probabilité relative aux entiers friables." Journal de théorie des nombres de Bordeaux 35, no. 2 (October 10, 2023): 481–93. http://dx.doi.org/10.5802/jtnb.1253.

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14

de la Bretèche, Régis, and Sary Drappeau. "Niveau de répartition des polynômes quadratiques et crible majorant pour les entiers friables." Journal of the European Mathematical Society 22, no. 5 (February 4, 2020): 1577–624. http://dx.doi.org/10.4171/jems/951.

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15

Tenenbaum, Gérald, and Jie Wu. "Moyennes de certaines fonctions multiplicatives sur les entiers friables." Journal für die reine und angewandte Mathematik (Crelles Journal) 2003, no. 564 (January 12, 2003). http://dx.doi.org/10.1515/crll.2003.087.

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16

Drappeau, Sary. "Remarques sur les moyennes des fonctions de Piltz sur les entiers friables." Quarterly Journal of Mathematics, September 26, 2016. http://dx.doi.org/10.1093/qmath/haw027.

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