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Institut de Mathématiques de Marseille, UMR 7373
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Automatic Sequences fulfill the Sarnak Conjecture

11h00 - 12h00
horaire FRUMAM

Aix-Marseille Université - Site St Charles
3, place Victor Hugo - case 39
13331 MARSEILLE Cedex 03

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 Mobius function.
In this talk we describe a method to reduce the treatment of automatic sequences to a structure combining synchronizing and invertible aspects.
We use (and adopt) 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.
I will try to explain the problem and give a rather long introduction - although there may be persons in the audience who know more about the sarnak conjecture and automatic sequences than me.