Disjointness of M\"{o}bius from asymptotically periodic functions

Fei Wei Yau Mathematical Sciences Center, Tsinghua University

Dynamical Systems Functional Analysis Number Theory mathscidoc:2205.11014

Pure and Applied Mathematics Quarterly, 2022.1
We investigate Sarnak's M\"obius Disjointness Conjecture through asymptotically periodic functions. It is shown that Sarnak's conjecture for rigid dynamical systems is equivalent to the disjointness of M\"obius from asymptotically periodic functions. We give sufficient conditions and a partial answer to the later one. As an application, we show that Sarnak's conjecture holds for a class of rigid dynamical systems, which improves an earlier result of Kanigowski-Lema{\'{n}}czyk-Radziwi{\l}{\l}.
Asymptotically periodic function, mean state, M\"{o}bius function, Sarnak's M\"{o}bius Disjointness Conjecture
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  title={Disjointness of M\"{o}bius from asymptotically periodic functions},
  author={Fei Wei},
  booktitle={Pure and Applied Mathematics Quarterly},
Fei Wei. Disjointness of M\"{o}bius from asymptotically periodic functions. 2022. In Pure and Applied Mathematics Quarterly. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220517165823019310243.
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