On completely multiplicative automatic sequences

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.

Cited by in corpus (1)

• A note on multiplicative automatic sequences, II