Polynomial mean complexity and logarithmic Sarnak conjecture

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.

Locations

• Ergodic Theory and Dynamical Systems - View
• arXiv (Cornell University) - View - PDF
• DataCite API - View