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 sequences that are generated by strongly connected automata where the initial state is fixed by the transition corresponding to $0$. 
Clemens M\"ullner
math.NT math.DS