A note on multiplicative automatic sequences

Oleksiy Klurman*, Pär Kurlberg*

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

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Abstract

We prove that any q-automatic completely multiplicative function 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.
Original languageEnglish
Pages (from-to)752-755
Number of pages4
JournalComptes Rendus Mathematique
Volume357
Issue number10
Early online date16 Oct 2019
DOIs
Publication statusE-pub ahead of print - 16 Oct 2019

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