English

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 {0,1}\{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 11-Fourier uniformity conjecture, where the frequencies are restricted to any subset of [0,1][0,1] 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}
}
R2 v1 2026-06-23T18:18:48.556Z