Moyennes effectives de fonctions multiplicatives complexes

Gérald Tenenbaum

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arXiv · 1709.01315

Moyennes effectives de fonctions multiplicatives complexes

Gérald Tenenbaum

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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.

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Gérald Tenenbaum. 2017-09-05. Moyennes effectives de fonctions multiplicatives complexes. https://arxiv.org/abs/1709.01315

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