Polynomial mean complexity and logarithmic Sarnak conjecture

被引：3
|
作者：
Huang, Wen [1 ]
Xu, Leiye [1 ]
Ye, Xiangdong [1 ]
机构：
[1] Univ Sci & Technol China, Hefei, Anhui, Peoples R China
来源：
ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2024年 / 44卷 / 03期
关键词：
Mobius function; topological dynamics; polynomial complexity; packing dimension; AVERAGED CHOWLA;
D O I：
10.1017/etds.2023.22
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：769 / 798
页数：30
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