A note on multiplicative automatic sequences

Oleksiy Klurman; Pär Kurlberg

doi:10.1016/j.crma.2019.10.002

A note on multiplicative automatic sequences

Oleksiy Klurman^*, Pär Kurlberg^*

^*Corresponding author for this work

School of Mathematics

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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 language	English
Pages (from-to)	752-755
Number of pages	4
Journal	Comptes Rendus Mathematique
Volume	357
Issue number	10
Early online date	16 Oct 2019
DOIs	https://doi.org/10.1016/j.crma.2019.10.002
Publication status	E-pub ahead of print - 16 Oct 2019

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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.",

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AU - Kurlberg, Pär

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AB - 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.

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DO - 10.1016/j.crma.2019.10.002

M3 - Article (Academic Journal)

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JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

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A note on multiplicative automatic sequences

Abstract

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