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