## Dynamical generalizations of the Prime Number Theorem and disjointness of additive and multiplicative actions

Florian Richter

Northwestern University

June 4, 2020

One of the fundamental challenges in number theory is to understand the intricate way in which the additive and multiplicative structures in the integers intertwine. We will explore a dynamical approach to this topic. After introducing a new dynamical framework for treating questions in multiplicative number theory, we will present an ergodic theorem which contains various classical number-theoretic results, such as the Prime Number Theorem, as special cases.