On multiplicative automatic sequences
Number Theory
2023-03-14 v3 Formal Languages and Automata Theory
Combinatorics
Abstract
We show that any automatic multiplicative sequence either coincides with a Dirichlet character or is identically zero when restricted to integers not divisible by small primes. This answers a question of Bell, Bruin and Coons. A similar result was obtained independently by Klurman and Kurlberg.
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Cite
@article{arxiv.1905.11981,
title = {On multiplicative automatic sequences},
author = {Jakub Konieczny},
journal= {arXiv preprint arXiv:1905.11981},
year = {2023}
}
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11 pages