Arbitrarily slow decay in the Möbius disjointness conjecture

DOI10.1017/etds.2022.61zbMath1526.37022arXiv2202.09491OpenAlexW4295213500WikidataQ114118472 ScholiaQ114118472MaRDI QIDQ6177384

Zhiren Wang, Amir Algom

Publication date: 31 August 2023

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.09491

zbMATH Keywords

topological dynamicsMöbius disjointnesszero topological entropy

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Ergodic theorems, spectral theory, Markov operators (37A30) Topological entropy (37B40) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) Relations between ergodic theory and number theory (37A44)

Cites Work

• Multiplicative functions in short intervals
• The Möbius function is strongly orthogonal to nilsequences
• On spectral disjointness of powers for rank-one transformations and Möbius orthogonality
• An averaged form of Chowla's conjecture
• Möbius disjointness for models of an ergodic system and beyond
• Sarnak's conjecture: what's new
• The logarithmic Sarnak conjecture for ergodic weights
• Flexibility of statistical properties for smooth systems satisfying the central limit theorem
• A counter-example for polynomial version of Sarnak's conjecture
• Disjointness of Moebius from Horocycle Flows
• Möbius disjointness along ergodic sequences for uniquely ergodic actions
• Prime number theorem for regular Toeplitz subshifts
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