Translator Disclaimer
15 November 2017 Automatic sequences fulfill the Sarnak conjecture
Clemens Müllner
Duke Math. J. 166(17): 3219-3290 (15 November 2017). DOI: 10.1215/00127094-2017-0024

Abstract

We present in this article a new method for dealing with automatic sequences. This method allows us to prove a Möbius 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.

Citation

Download Citation

Clemens Müllner. "Automatic sequences fulfill the Sarnak conjecture." Duke Math. J. 166 (17) 3219 - 3290, 15 November 2017. https://doi.org/10.1215/00127094-2017-0024

Information

Received: 4 May 2016; Revised: 21 April 2017; Published: 15 November 2017
First available in Project Euclid: 5 October 2017

zbMATH: 06825580
MathSciNet: MR3724218
Digital Object Identifier: 10.1215/00127094-2017-0024

Subjects:
Primary: 11A63
Secondary: 11B85, 11L20, 11N05, 37B10

Rights: Copyright © 2017 Duke University Press

JOURNAL ARTICLE
72 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.166 • No. 17 • 15 November 2017
Back to Top