Moyennes effectives de fonctions multiplicatives complexes

TL;DR

This paper develops effective mean-value estimates for complex multiplicative functions, providing quantitative versions of classical results and extending previous work, with applications in prime factor distribution and additive functions.

Contribution

It introduces essentially optimal effective mean-value estimates for a broad class of multiplicative functions, extending Wirsing's and Halász's classical results with new applications.

Findings

Provides effective bounds for mean-values of multiplicative functions

Extends classical estimates to broader classes of functions

Applies results to prime factor distribution and additive functions

Abstract

We establish effective mean-value estimates for a wide class of multiplicative arithmetic functions, thereby providing (essentially optimal) quantitative versions of Wirsing's classical estimates and extending those of Hal\'asz. Several applications are derived, including: estimates for the difference of mean-values of so-called pretentious functions, local laws for the distribution of prime factors in an arbitrary set, and weighted distribution of additive functions.