A note on multiplicative automatic sequences, II

Oleksiy Klurman; Pär Kurlberg

doi:10.1112/blms.12318

A note on multiplicative automatic sequences, II

Oleksiy Klurman, Pär Kurlberg

School of Mathematics

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Abstract

We prove that any 푞 ‐automatic multiplicative function 푓:ℕ→ℂ either essentially coincides with a Dirichlet character, or vanishes on all sufficiently large primes. This confirms a strong form of a conjecture of Bell, Bruin and Coons [Trans. Amer. Math. Soc. 364 (2012) 933–959].

Original language	English
Pages (from-to)	185-188
Number of pages	4
Journal	Bull. Lond. Math. Soc.
Volume	52
Issue number	1
Early online date	23 Jan 2020
DOIs	https://doi.org/10.1112/blms.12318
Publication status	Published - 24 Feb 2020

Keywords

11B85 (primary)
68R15 (secondary)

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10.1112/blms.12318

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Wiley at https://londmathsoc.onlinelibrary.wiley.com/doi/full/10.1112/blms.12318 . Please refer to any applicable terms of use of the publisher.
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AB - We prove that any 푞 ‐automatic multiplicative function 푓:ℕ→ℂ either essentially coincides with a Dirichlet character, or vanishes on all sufficiently large primes. This confirms a strong form of a conjecture of Bell, Bruin and Coons [Trans. Amer. Math. Soc. 364 (2012) 933–959].

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KW - 68R15 (secondary)

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DO - 10.1112/blms.12318

M3 - Article (Academic Journal)

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JF - Bull. Lond. Math. Soc.

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A note on multiplicative automatic sequences, II

Abstract

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