On completely multiplicative automatic sequences (1903.04385v3)

Abstract: In this article we prove that all completely multiplicative automatic sequences $(a_n){n \in \mathbf{N}}$ defined on $\mathbf{C}$, vanishing or not, can be written in the form $a_n=b_n\chi_n$ where $(b_n){n \in \mathbf{N}}$ is an almost constant sequence, and $(\chi_n)_{n \in \mathbf{N}}$ is a Dirichlet character.