All automatic sequences satisfy the full Sarnak conjecture

Clemens Müllner
Vienna University of Technology, Austria
http://math.univ-lyon1.fr/~mullner/

Date(s) : 23/02/2016   iCal
11 h 05 min - 12 h 00 min

We use analytic tools to prove that the dynamical system corresponding to any automatic sequence fulfils the Sarnak conjecture.
In particular, any complex valued automatic sequence is orthogonal to the Moebius function.
In this talk, we develop a new method to reduce the treatment of automatic sequences to a structure combining synchronizing and invertible aspects.

We use (and adapt) a method developed by Mauduit and Rivat, as well as combine ideas for invertible automata by Drmota and Morgenbesser and synchronizing automata by Deshouillers, Drmota and myself.

Furthermore, we prove a prime number theorem for many automatic sequences.

https://arxiv.org/abs/1602.03042

 

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