Asymptotic orthogonality of powers of measure-preserving automorphisms and multiplicative functions

Speaker(s)

Mariusz Lemańczyk

Affiliation

Uniwersytet Mikołaja Kopernika

Date

April 1, 2016, 10:15 a.m.

Room

room 5840

Seminar

Seminar of Dynamical Systems Group

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An automorphism T is called to have asymptotically orthogonal powers (AOP), if its different prime powers T^p and T^q become closer and closer to be disjoint in the sense of Furstenberg when p,q\to\infty. I will show that the AOP property is achieved in many classical classes of automorphisms, for example: quasi-discrete spectrum automorphisms, nil-rotations and some systems of number theoretic origin. I will also show how the AOP property of uniquely ergodic T is used to show that the observables f(T^{n}x), n\in\N, are orthogonal to any multiplicative arithmetic function u:\N\to\C, |u|\leq1 on so called typical short interval.

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