Moyennes effectives de fonctions multiplicatives complexes
Number Theory
2025-07-23 v13
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.
Cite
@article{arxiv.1709.01315,
title = {Moyennes effectives de fonctions multiplicatives complexes},
author = {Gérald Tenenbaum},
journal= {arXiv preprint arXiv:1709.01315},
year = {2025}
}
Comments
in French, contains corrections with respect to the published version