Moyennes de certaines fonctions multiplicatives sur les entiers friables, 3

TL;DR

This paper studies logarithmic averages of multiplicative functions over friable integers, providing improved estimates and error terms under classical sieve assumptions, with applications to prime power sieves.

Contribution

It offers sharper estimates for averages of multiplicative functions over friable integers under classical sieve hypotheses, enhancing previous results.

Findings

Improved bounds on logarithmic averages of multiplicative functions.

Enhanced error term estimates in the context of friable integers.

Application to effective prime power sieves.

Abstract

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.