Dynamical systems and uniform distribution of sequences

TL;DR

This paper surveys how dynamical systems are applied to number theory, especially in understanding normal numbers and uniform distribution, and introduces a new condition for multidimensional van der Corput sets.

Contribution

It presents a new sufficient condition for multidimensional van der Corput sets and applies it to various examples, advancing the understanding of uniform distribution in number theory.

Findings

Established a new sufficient condition for multidimensional van der Corput sets

Applied the condition to multiple examples in number theory

Enhanced understanding of normal numbers and uniform distribution

Abstract

We give a survey on classical and recent applications of dynamical systems to number theoretic problems. In particular, we focus on normal numbers, also including computational aspects. The main result is a sufficient condition for establishing multidimensional van der Corput sets. This condition is applied to various examples.