# A note on multiplicative automatic sequences

@article{Klurman2019ANO,
title={A note on multiplicative automatic sequences},
author={Oleksiy Klurman and P. Kurlberg},
journal={Comptes Rendus Mathematique},
year={2019},
volume={357},
pages={752-755}
}
• Published 2019
• Mathematics
• Comptes Rendus Mathematique
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 J. Bell, N. Bruin and M. Coons for completely multiplicative functions. Further, assuming GRH, the methods allow us to replace completely multiplicative functions with multiplicative functions.
A note on multiplicative automatic sequences
• Mathematics
• 2019
We prove that any $q$-automatic completely multiplicative function $f:\mathbb{N}\to\mathbb{C}$ essentially coincides with a Dirichlet character. This answers a question of J. P. Allouche and L.Expand
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• Mathematics
• 2021
Automatic sequences have many properties that other sequences (in particular, non-uniformly morphic sequences) do not necessarily share. In this paper we survey a number of different methods that canExpand
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We obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.
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We obtain a complete classification of complex-valued sequences which are both multiplicative and automatic.

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