Automatic sequences fulfill the Sarnak conjecture
Number Theory
2018-02-21 v3 Dynamical Systems
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 .
Cite
@article{arxiv.1602.03042,
title = {Automatic sequences fulfill the Sarnak conjecture},
author = {Clemens Müllner},
journal= {arXiv preprint arXiv:1602.03042},
year = {2018}
}
Comments
55 pages