Polynomial mean complexity and Logarithmic Sarnak conjecture
Dynamical Systems
2020-09-07 v1
Abstract
In this paper, we reduce the logarithmic Sarnak conjecture to the -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 -Fourier uniformity conjecture, where the frequencies are restricted to any subset of with packing dimension less than one.
Keywords
Cite
@article{arxiv.2009.02090,
title = {Polynomial mean complexity and Logarithmic Sarnak conjecture},
author = {Wen Huang and Leiye Xu and Xiangdong Ye},
journal= {arXiv preprint arXiv:2009.02090},
year = {2020}
}