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arXiv · 2004.04766

Multiplicative functions in large arithmetic progressions and applications

Étienne Fouvry·Gérald Tenenbaum
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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 Erd{\H o}s-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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Étienne Fouvry, Gérald Tenenbaum. 2020-04-09. Multiplicative functions in large arithmetic progressions and applications. https://arxiv.org/abs/2004.04766

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