ﻻ يوجد ملخص باللغة العربية
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.
In this paper, we show that for any sequence ${bf a}=(a_n)_{nin Z}in {1,ldots,k}^mathbb{Z}$ and any $epsilon>0$, there exists a Toeplitz sequence ${bf b}=(b_n)_{nin Z}in {1,ldots,k}^mathbb{Z}$ such that the entropy $h({bf b})leq 2 h({bf a})$ and $lim
We construct the counter-example for polynomial version of Sarnaks conjecture for minimal systems, which assets that the Mobius function is linearly disjoint from subsequences along polynomials of deterministic sequences realized in minimal systems.
In this paper we study $C^*$-algebra version of Sarnak Conjecture for noncommutative toral automorphisms. Let $A_Theta$ be a noncommutative torus and $alpha_Theta$ be the noncommutative toral automorphism arising from a matrix $Sin GL(d,mathbb{Z})$.
We study dynamical systems that have bounded complexity with respect to three kinds of directional metrics: the directional Bowen metric $d_k^{vec{v},b}$, the directional max-mean metric $hat{d}_k^{vec{v},b}$ and the directional mean metric $overline
Assuming Schanuels conjecture, we prove that any polynomial exponential equation in one variable must have a solution that is transcendental over a given finitely generated field. With the help of some recent results in Diophantine geometry, we obtai