A note on multiplicative automatic sequences, II

Klurman, Oleksiy; Kurlberg, Pär

doi:10.1112/blms.12318

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A note on multiplicative automatic sequences, II

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Klurman, Oleksiy
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1112/blms.12318
(Publisher version)

https://doi.org/10.48550/arXiv.1905.10897
(Preprint)

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Citation

Klurman, O., & Kurlberg, P. (2020). A note on multiplicative automatic sequences, II. Bulletin of the London Mathematical Society, 52(1), 185-188. doi:10.1112/blms.12318.

Cite as: https://hdl.handle.net/21.11116/0000-0009-9061-6

Abstract

We prove that any $q$-automatic multiplicative function
$f:\mathbb{N}\to\mathbb{C}$ either essentially coincides with a Dirichlet
character, or vanishes on all sufficiently large primes. This confirms a strong
form of a conjecture of J. Bell, N. Bruin, and M. Coons.