## EVENT DETAILS AND ABSTRACT

**Dynamical Systems Seminar**
**Title:** Ergodicity of the Liouville system implies the Chowla conjecture

**Speaker:** Nikos Frantzikinakis

**Speaker Info:** University of Crete

**Brief Description:**

**Special Note**:

**Abstract:**

The Liouville function assigns the value one to integers with an even number of prime factors and minus one elsewhere.
Its importance stems from the fact that several well known conjectures in number theory can be rephrased as conjectural properties
of the Liouville function. A conjecture of Chowla asserts that the signs of the Liouville function are distributed randomly on the integers,
that is, they form a normal sequence of plus and minus ones. Reinterpreted in the language of ergodic theory this conjecture asserts
that the "Liouville system" is a Bernoulli system. We prove that a much weaker property, namely, ergodicity of the "Liouville system",
implies the Chowla conjecture. Our argument combines techniques from ergodic theory, analytic number theory, and higher order
Fourier analysis.

**Date:** Tuesday, April 11, 2017

**Time:** 4:00pm

**Where:** Lunt 104

**Contact Person:** Prof. Bryna Kra

**Contact email:** kra@math.northwestern.edu

**Contact Phone:** 847-491-5567

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