论文标题

多项式平均复杂性和对数sarnak猜想

Polynomial mean complexity and Logarithmic Sarnak conjecture

论文作者

Huang, Wen, Xu, Leiye, Ye, Xiangdong

论文摘要

在本文中,我们将对数SARNAK猜想减少到具有多项式平均复杂性的$ \ {0,1 \} $ - 符号系统。通过证明对数SARNAK的猜想可以适用于具有均方根复杂性的任何拓扑动态系统,我们提供了$ 1 $ fourier的均匀性猜想的一种变体,其中频率仅限于$ [0,1]的任何子集,包装尺寸小于一个。

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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