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Moyennes effectives de fonctions multiplicatives complexes

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 Halász. 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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Contributor : Gérald Tenenbaum Connect in order to contact the contributor
Submitted on : Wednesday, November 24, 2021 - 12:42:52 AM
Last modification on : Wednesday, January 5, 2022 - 2:19:51 PM


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Gérald Tenenbaum. Moyennes effectives de fonctions multiplicatives complexes. Ramanujan Journal, Springer Verlag, 2017, 44 (3), pp.641-701. ⟨10.1007/s11139-017-9949-7⟩. ⟨hal-01300328v19⟩



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