A note on multiplicative automatic sequences
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DOI: 10.1016/j.crma.2019.10.002
Abstract: Abstract We prove that any q-automatic completely multiplicative function f : N → C essentially coincides with a Dirichlet character. This answers a question of J.-P. Allouche and L. Goldmakher and confirms a conjecture of… read more here.
Keywords: automatic sequences; multiplicative automatic; multiplicative functions; completely multiplicative ... See more keywords
On completely multiplicative automatic sequences
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DOI: 10.1016/j.jnt.2019.12.015
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… read more here.
Keywords: completely multiplicative; multiplicative automatic; automatic sequences;