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Article Dans Une Revue Transactions of the American Mathematical Society Année : 2022

Multiplicative functions in large arithmetic progressions and applications

Résumé

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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Dates et versions

hal-03167173 , version 1 (11-03-2021)
hal-03167173 , version 2 (22-03-2021)

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Étienne Fouvry, Gérald Tenenbaum. Multiplicative functions in large arithmetic progressions and applications. Transactions of the American Mathematical Society, inPress, 375 (1), pp.245-299. ⟨10.1090/tran/8442⟩. ⟨hal-03167173v2⟩
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