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arXiv · 2009.02090

Polynomial mean complexity and Logarithmic Sarnak conjecture

Wen Huang·Leiye Xu·Xiangdong Ye
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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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Wen Huang, Leiye Xu, Xiangdong Ye. 2020-09-04. Polynomial mean complexity and Logarithmic Sarnak conjecture. https://arxiv.org/abs/2009.02090

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