Some ergodic properties of multiplicative functions

Vortrag von Prof. Dr. Bernard Host

Datum: 04.11.19  Zeit: 14.00 - 15.00  Raum: ETH HG G 43 CANCELLED

The Furstenberg Correspondence Principle links "combinatorial" properties of a function defined on the integers with the properties of some measure preserving systems, called the Furstenberg systems associated to this function. We study such systems for multiplicative functions, in particular for the Möbius and Liouville functions, and give applications in the direction of the Chowla and Sarnak Conjectures. We present first an overview of some recent results of Tao and coauthors. Then we give a structural result about these systems, some applications, and we conclude with some ideas of the proof. This is a joint work with Nikos Frantzikinakis.