Automatic sequences are orthogonal to aperiodic multiplicative functions

Mariusz Lemańczyk, Clemens Müllner

Given a finite alphabet $\mathbb{A}$ and a primitive substitution $\theta :\mathbb{A}\to {\mathbb{A}}^{\lambda }$ (of constant length $\lambda$), let $(X_{\theta },S)$ denote the corresponding dynamical system, w…