Arbitrarily slow decay in the Möbius disjointness conjecture

Amir Algom, Zhiren Wang

Research output: Contribution to journalArticlepeer-review


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 anbut does not.

Original languageEnglish
Pages (from-to)2863-2880
Number of pages18
JournalErgodic Theory and Dynamical Systems
Issue number9
StatePublished - 9 Sep 2023

Bibliographical note

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


  • Möbius disjointness
  • topological dynamics
  • zero topological entropy

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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