Multiplicative functions in large arithmetic progressions and applications

Fouvry, Étienne; Tenenbaum, Gérald

doi:10.1090/tran/8442

Multiplicative functions in large arithmetic progressions and applications
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by Étienne Fouvry and Gérald Tenenbaum PDF

Trans. Amer. Math. Soc. 375 (2022), 245-299 Request permission

Abstract:

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 $\tau (n-1)$ where $\tau$ denotes the divisor function.

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