Arbitrarily slow decay in the Möbius disjointness conjecture

Amir Algom, Zhiren Wang

Research output: Contribution to journalArticlepeer-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 anbut does not.

Original languageEnglish (US)
Pages (from-to)2863-2880
Number of pages18
JournalErgodic Theory and Dynamical Systems
Volume43
Issue number9
DOIs
StatePublished - Sep 9 2023

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics

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