Automatic sequences are orthogonal to aperiodic multiplicative functions

Clemens Müllner
Institut Camille Jordan (ICJ), Villeurbanne
http://math.univ-lyon1.fr/~mullner/

Date(s) : 27/11/2018   iCal
11 h 00 min - 12 h 00 min

Recently it was shown by the author that all automatic sequences satisfy the Sarnak conjecture. In particular, they are orthogonal to the Möbius function. This result relied on a structural result for automata and tools from analytic number theory, most importantly a method developed by Mauduit and Rivat.
In this talk we give an interpretation of the mentioned structural result in terms of substitutions and dynamical systems. Furthermore, we use joinings and a criterion by Katai to show that any primitive substitution/automatic sequence is orthogonal not just to the Möbius function but to any bounded aperiodic multiplicative function.
This is joint work with Mariusz Lemanczyk.

https://arxiv.org/abs/1811.00594

 

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