Arbitrarily slow decay in the Möbius disjointness conjecture

Amir Algom; Zhiren Wang

doi:10.1017/etds.2022.61

Arbitrarily slow decay in the Möbius disjointness conjecture

Amir Algom, Zhiren Wang

Department of Mathematics, Physics and Computer Science (Oranim Campus)

Research output: Contribution to journal › Article › peer-review

Abstract

Sarnak's Möbius disjointness conjecture asserts that for any zero entropy dynamical system, for every and every. We construct examples showing that this can go to zero arbitrarily slowly. In fact, our methods yield a more general result, where in lieu of, one can put any bounded sequence such that the Cesàro mean of the corresponding sequence of absolute values does not tend to zero. Moreover, in our construction, the choice of x depends on the sequence a_nbut does not.

Original language	English
Pages (from-to)	2863-2880
Number of pages	18
Journal	Ergodic Theory and Dynamical Systems
Volume	43
Issue number	9
DOIs	https://doi.org/10.1017/etds.2022.61
State	Published - 9 Sep 2023

Bibliographical note

Publisher Copyright:
© The Author(s), 2022. Published by Cambridge University Press.

Keywords

Möbius disjointness
topological dynamics
zero topological entropy

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1017/etds.2022.61

Cite this

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abstract = "Sarnak's M{\"o}bius disjointness conjecture asserts that for any zero entropy dynamical system, for every and every. We construct examples showing that this can go to zero arbitrarily slowly. In fact, our methods yield a more general result, where in lieu of, one can put any bounded sequence such that the Ces{\`a}ro mean of the corresponding sequence of absolute values does not tend to zero. Moreover, in our construction, the choice of x depends on the sequence anbut does not.",

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Arbitrarily slow decay in the Möbius disjointness conjecture

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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