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

Florian Richter, Northwestern University

Please not the time change for this seminar

Zoom link:


Password: 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.