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Séminaire Combinatoire et Théorie des Nombres ICJ

# Automatic Sequences fulfill the Sarnak Conjecture

## by Clemens Müllner (Université Claude Bernard - Lyon 1)

mardi 16 janvier 2018 de au (Europe/Paris)
at ICJ ( Bât. Braconnier, salle Fokko du Cloux )
 Description We use analytic tools to prove that the dynamical system corresponding to any automatic sequence fulfills 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.