Multiplicative functions in large arithmetic progressions and\n applications

2020/04/09 by Étienne Fouvry, Gérald Tenenbaum, Fouvry, Étienne +1
Mathematics · #11N36 #11N60 #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT) #Primary: 11N37 #Secundary: 11N25

paper · pdf · doi:10.48550/arxiv.2004.04766

openalex publication_date 2020/04/09 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

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

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• A lower bound for the variance in arithmetic progressions of some\n multiplicative functions close to 1
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• Moyennes effectives de fonctions multiplicatives complexes
• A note on multiplicative functions on progressions to large moduli