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Moyennes de certaines fonctions multiplicatives sur les entiers friables, 3

Part of: Polynomials and matrices Multiplicative number theory

Published online by Cambridge University Press:  01 March 2008

Gérald Tenenbaum  and
Jie Wu
Gérald Tenenbaum
Affiliation:
Institut Élie Cartan, UMR 7502, Université Henri Poincaré–Nancy 1, BP 239, 54506 Vandœuvre-lès-Nancy, France (email: [email protected], [email protected])
Jie Wu
Affiliation:
Institut Élie Cartan, UMR 7502, Université Henri Poincaré–Nancy 1, BP 239, 54506 Vandœuvre-lès-Nancy, France (email: [email protected], [email protected])
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Abstract

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We 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.

Keywords

friable integersSelberg’s sievelogarithmic averages of multiplicative functions

MSC classification

Secondary: 11N25: Distribution of integers with specified multiplicative constraints 11N35: Sieves 11N36: Applications of sieve methods 11N56: Rate of growth of arithmetic functions 11C08: Polynomials
Type
Research Article
Information
Compositio Mathematica , Volume 144 , Issue 2 , March 2008 , pp. 339 - 376
Copyright
Copyright © Foundation Compositio Mathematica 2008