Van der Corput's Difference Theorem: some modern developments

TL;DR

This paper reviews modern developments of van der Corput's difference theorem, highlighting its applications and connections across uniform distribution, ergodic theory, topological dynamics, and combinatorics.

Contribution

It synthesizes recent advancements and explores new applications of the classical theorem in various mathematical fields.

Findings

Enhanced understanding of the theorem's role in uniform distribution

New connections established with ergodic theory and topological dynamics

Potential applications in combinatorics and related areas

Abstract

We discuss various forms of the classical van der Corput's difference theorem and explore applications to and connections with the theory of uniform distribution, ergodic theory, topological dynamics and combinatorics.