On completely multiplicative automatic sequences
Shuo Li · arXiv (Cornell University) · 2019
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 $a_n=b_nχ_n$ where $(b_n)_{n \in \mathbf{N}}$ is an almost constant sequence, and $(χ_n)_{n \in \mathbf{N}}$ is a Dirichlet character.