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arXiv · 1602.03042

Automatic sequences fulfill the Sarnak conjecture

Clemens Müllner
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Abstract

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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Clemens Müllner. 2016-02-09. Automatic sequences fulfill the Sarnak conjecture. https://doi.org/10.1215/00127094-2017-0024

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