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Une nouvelle approche dans la théorie des entiers friables

Part of: Multiplicative number theory

Published online by Cambridge University Press:  20 February 2017

Régis de la Bretèche  and
Gérald Tenenbaum
Régis de la Bretèche
Affiliation:
Université Paris Diderot – Paris 7, Sorbonne Paris Cité, UMR 7586, Institut de Mathématiques de Jussieu-PRG, Case 7012, F-75013 Paris, France email regis.delabreteche@imj-prg.fr
Gérald Tenenbaum
Affiliation:
Institut Élie Cartan, Université de Lorraine, BP 70239, F-54506 Vandœuvre-lès-Nancy Cedex, France email gerald.tenenbaum@univ-lorraine.fr
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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.

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.

Keywords

Entiers friablesméthode du colinégalité de Montgomery–Wirsingprincipe de transfertrégion sans zérosommes d’exponentielles sur les nombres premiers

MSC classification

Primary: 11N25: Distribution of integers with specified multiplicative constraints 11N37: Asymptotic results on arithmetic functions
Type
Research Article
Information
Compositio Mathematica , Volume 153 , Issue 3 , March 2017 , pp. 453 - 473
Copyright
© The Authors 2017 

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