Multiplicative functions in large arithmetic progressions and applications
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- by Étienne Fouvry and Gérald Tenenbaum PDF
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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 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.References
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Additional Information
- Étienne Fouvry
- Affiliation: Université Paris–Saclay, CNRS, Laboratoire de Mathématiques d’Orsay, 91405 Orsay, France
- ORCID: 0000-0002-1840-9467
- Email: Etienne.Fouvry@universite-paris-saclay.fr
- Gérald Tenenbaum
- Affiliation: Institut Élie Cartan, Université de Lorraine, B.P. 70239, F–54506 Vandœuvre-lès-Nancy Cedex, France
- ORCID: 0000-0002-0478-3693
- Email: Gerald.Tenenbaum@univ-lorraine.fr
- Received by editor(s): June 5, 2020
- Received by editor(s) in revised form: January 22, 2021, and March 9, 2021
- Published electronically: October 8, 2021
- © Copyright 2021 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 375 (2022), 245-299
- MSC (2020): Primary 11N37; Secondary 11N25, 11N36, 11N60
- DOI: https://doi.org/10.1090/tran/8442
- MathSciNet review: 4358667