05/04: Nikos Frantzikinakis
Ergodic properties of bounded multiplicative functions and applications
Abstract: The Möbius and the Liouville function are multiplicative functions that encode important information related to distributional properties of the prime numbers. It is widely believed that their non-zero values fluctuate between plus and minus one in a random way, and two conjectures in this direction, one by Chowla and another by Sarnak, have attracted a lot of interest in recent years. In this talk, we shall see how one can make progress towards these conjectures by using ergodic theory in order to analyze feedback originating from analytic number theory. It turns out that key to the success of this method is an in depth understanding of structural properties of measure preserving systems naturally associated with bounded multiplicative functions. I will present what is known and what remains to be determined about such systems. The talk is based on joint work with Bernard Host.