Furstenberg Systems of Bounded Multiplicative Functions and Applications

DOI10.1093/imrn/rnz037zbMath1483.37006arXiv1804.08556OpenAlexW2963036827MaRDI QIDQ3382636

Nikos Frantzikinakis, Bernard Host

Publication date: 21 September 2021

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.08556

zbMATH Keywords

multiplicative functionsmeasure-preserving systemsChowla conjectureinfinite-step nilsystems

Mathematics Subject Classification ID

Dynamical aspects of measure-preserving transformations (37A05) Asymptotic results on arithmetic functions (11N37) Ergodic theorems, spectral theory, Markov operators (37A30) Relations between ergodic theory and number theory (37A44)

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An ergodic correspondence principle, invariant means and applications ⋮ On Furstenberg systems of aperiodic multiplicative functions of Matomäki, Radziwiłł, and Tao ⋮ On arithmetic functions orthogonal to deterministic sequences ⋮ Sarnak's conjecture for nilsequences on arbitrary number fields and applications ⋮ Juxtaposing combinatorial and ergodic properties of large sets of integers ⋮ The structure of correlations of multiplicative functions at almost all scales, with applications to the Chowla and Elliott conjectures ⋮ Good weights for the Erd\H{o}s discrepancy problem ⋮ Automatic sequences are orthogonal to aperiodic multiplicative functions ⋮ Furstenberg systems of Hardy field sequences and applications

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