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arXiv · 1904.04337

A note on multiplicative automatic sequences

Oleksiy Klurman·Pär Kurlberg
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Abstract

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. Goldmakher and confirms a conjecture of J. Bell, N. Bruin and M. Coons for completely multiplicative functions. Further, assuming two standard conjectures in number theory, the methods allows for removing the assumption of completeness.

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Oleksiy Klurman, Pär Kurlberg. 2019-04-08. A note on multiplicative automatic sequences. https://arxiv.org/abs/1904.04337

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