Automatic sequences fulfill the Sarnak conjecture

Automatic sequences fulfill the Sarnak conjecture

We present in this paper a new method to deal with automatic sequences. This method allows us to prove a M\"obius-randomness-principle for automatic sequences from which we deduce the Sarnak conjecture for this class of sequences. Furthermore, we can show a Prime Number Theorem for automatic se...

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Veröffentlicht in:arXiv.org 2017-07
1. Verfasser: Müllner, Clemens
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Mathematics - Dynamical Systems
Mathematics - Number Theory
Sequences
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description We present in this paper a new method to deal with automatic sequences. This method allows us to prove a M\"obius-randomness-principle for automatic sequences from which we deduce the Sarnak conjecture for this class of sequences. Furthermore, we can show a Prime Number Theorem for automatic sequences that are generated by strongly connected automata where the initial state is fixed by the transition corresponding to \(0\).
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subjects Mathematics - Dynamical Systems
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Sequences
title Automatic sequences fulfill the Sarnak conjecture
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