Théorème d'Erdős-Kac pour les translatés d'entiers ayant k facteurs premiers

Goudout, Élie

doi:10.1016/j.jnt.2019.09.012

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2021

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“…This result generalizes to a natural framework a recent work of Goudout [12] in which f = ω. When k = 1, it follows from a general theorem of Barban, Vinogradov and Levin [1].…”

Section: )supporting

confidence: 81%

Multiplicative functions in large arithmetic progressions and applications

Fouvry¹,

Tenenbaum

2021

Trans. Amer. Math. Soc.

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We establish new Bombieri-Vinogradov type estimates for a wide class of multiplicative arithmetic functions and derive several applications, including: a new proof of a recent estimate by Drappeau and Topacogullari for arithmetical correlations; a theorem of Erdős-Wintner type with support equal to the level set of an additive function at shifted argument; and a law of iterated logarithm for the distribution of prime factors of integers weighted by τ (n − 1) where τ denotes the divisor function.

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“…This result generalizes to a natural framework a recent work of Goudout [12] in which f = ω. When k = 1, it follows from a general theorem of Barban, Vinogradov and Levin [1].…”

Section: )supporting

confidence: 81%