In this paper, we investigate asymptotically periodic functions from the
point of view of operator algebra and dynamical systems. To study the
M\"{o}bius disjointness of these functions, we prove a general result on the
averages of multiplicative functions in short arithmetic progressions. As an
application, we show that Sarnak's M\"{o}bius Disjointness Conjecture holds for
certain topological dynamical systems.Comment: 46 page

Wei, Fei

English

arXiv

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}.Comment: 47 pages, this paper was recently published in Pure and Applied
  Mathematics Quarterl

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

Abstract

Similar works

Full text

Available Versions

arXiv.org e-Print Archive