Sarnak's conjecture for rank-one subshifts

2021/09/02 by Mahmood Etedadialiabadi, Etedadialiabadi, Mahmood, Su Gao +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #math.DS #math.NT #msc:37A45 #msc:37B20

paper · pdf · doi:10.48550/arxiv.2109.01200

12 pages

arxiv created 2021/09/02 · arxiv updated 2021/09/06

Abstract

Using techniques developed in \citeKLR, we verify Sarnak's conjecture for two classes of rank-one subshifts with unbounded cutting parameters. The first class of rank-one subshifts we consider are called \em almost complete congruency classes (\em accc), the definition of which is motivated by the main result of \citeGS, which implies that, when a rank-one subshift carries a unique non-atomic invariant probability measure, it is accc if it is measure-theoretically isomorphic to an odometer. The second class we consider consists of Katok's map and its generalizations.

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