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

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

**Please not the time change for this seminar**

**Zoom link:**

https://theias.zoom.us/j/959183254

**Passw ord: **

**the three digit integer that is the cube of the sum of its digits**

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. This naturally leads to a formulation of an extended form of Sarnak's conjecture, which deals with the disjointness of actions of (N,+) and (N,*). This talk is based on joint work with Vitaly Bergelson.