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

Abstract: 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 $(\mathbb{N},+)$ and $(\mathbb{N},*)$. This talk is based on joint work with Vitaly Bergelson.

dynamical systems

Audience: researchers in the topic

Torun ETDS online seminar

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