Moyennes de certaines fonctions multiplicatives sur les entiers friables, 3

Gérald Tenenbaum (1) , Jie Wu (1)

1 IECN - Institut Élie Cartan de Nancy

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 Gallagher-Selberg prime power sieve.

Mots clés: friable integers; sieve; Selberg sieve; Ghallager sieve; prime power sieve; mean value of arithmetic functions; weighted mean values; logarithmic mean values; prime power sieve.

Domaines: Théorie des nombres [math.NT]

Gérald Tenenbaum, Jie Wu. Moyennes de certaines fonctions multiplicatives sur les entiers friables, 3. Compositio Mathematica, 2008, 144, pp.339-376. ⟨hal-00131532v4⟩