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Une nouvelle approche dans la théorie des entiers friables

  • Régis de la Bretèche (a1) and Gérald Tenenbaum (a2)
Abstract

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.

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.

Grâce à une nouvelle approche, dont le point de départ est un calcul de résidu, nous précisons certaines des estimations connues pour la fonction de comptage des entiers friables. Le gain se révèle crucial pour diverses applications, dont certaines concernent des questions fondamentales de la théorie probabiliste des nombres.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

R. de la Bretèche and G. Tenenbaum , Propriétés statistiques des entiers friables , Ramanujan J. 9 (2005), 139202.

R. de la Bretèche and G. Tenenbaum , Entiers friables : inégalité de Turán–Kubilius et applications , Invent. Math. 159 (2005), 531588.

R. de la Bretèche and G. Tenenbaum , Sur l’inégalité de Turán–Kubilius friable , J. Lond. Math. Soc. (2) 93 (2016), 175193.

N. G. de Bruijn , On the number of positive integers ⩽x and free of prime factors > y , Nederl. Akad. Wetensch. Proc. Ser. A 54 (1951), 5060; Indag. Math. 13 (1951), 50–60.

N. G. de Bruijn , On the number of positive integers ⩽x and free of prime factors > y, II , Nederl. Akad. Wetensch. Proc. Ser. A 69 (1966), 239247.

G. Hanrot , B. Martin and G. Tenenbaum , Constantes de Turán–Kubilius friables : étude numérique , Exp. Math. 19 (2010), 345361.

A. Hildebrand , Integers free of large prime factors and the Riemann hypothesis , Mathematika 31 (1984), 258271.

A. Hildebrand , On the number of positive integers ⩽x and free of prime factors > y , J. Number Theory 22 (1986), 289307.

A. Hildebrand and G. Tenenbaum , On integers free of large prime factors , Trans. Amer. Math. Soc. 296 (1986), 265290.

A. Hildebrand and G. Tenenbaum , Integers without large prime factors , J. Théor. Nombres Bordeaux 5 (1993), 411484.

H. L. Montgomery , Ten lectures on the interface between analytic number theory and harmonic analysis, CBMS Regional Conference Series in Mathematics, vol. 84, published for the Conference Board of the Mathematical Sciences, Washington, DC (American Mathematical Society, Providence, RI, 1994).

O. Robert and G. Tenenbaum , Sur la répartition du noyau d’un entier , Indag. Math. 24 (2013), 802914.

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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
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