Disjointness of Möbius from asymptotically periodic functions

Abstract

We investigate Sarnak's Möbius Disjointness Conjecture through asymptotically periodic functions. It is shown that Sarnak's conjecture for rigid dynamical systems is equivalent to the disjointness of Möbius 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{ń}czyk-Radziwiłł.

47 pages, this paper was recently published in Pure and Applied Mathematics Quarterly

References in corpus (8)

• Möbius disjointness for topological models of ergodic systems with discrete spectrum
• Rigidity in dynamics and Möbius disjointness
• Multiplicative functions in short arithmetic progressions
• Measure complexity and Möbius disjointness
• Quasi-graphs, zero entropy and measures with discrete spectrum
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Cited by in corpus (3)

• Multiplicative functions in short arithmetic progressions
• Anqie entropy and arithmetic compactification of natural numbers
• Sarnak's Möbius disjointness for dynamical systems with singular spectrum and dissection of Möbius flow