Polynomial mean complexity and Logarithmic Sarnak conjecture

2020/09/04 by Huang, Wen, Xu, Leiye, Ye, Xiangdong · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2009.02090

Abstract

In this paper, we reduce the logarithmic Sarnak conjecture to the \0,1\-symbolic systems with polynomial mean complexity. By showing that the logarithmic Sarnak conjecture holds for any topologically dynamical system with sublinear complexity, we provide a variant of the 1-Fourier uniformity conjecture, where the frequencies are restricted to any subset of [0,1] with packing dimension less than one.

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• Almost Countable Spectrum and Logarithmic Sarnak Conjecture

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