Weyl's uniform distribution under periodic perturbation

TL;DR

This paper investigates how periodic perturbations affect Weyl's uniform distribution theory, revealing that conditions for density and uniform distribution modulo 1 differ from classical cases.

Contribution

It extends Weyl's uniform distribution theory to include periodic perturbations, identifying new conditions for density and uniform distribution.

Findings

Conditions for (mod 1) density differ with periodic perturbation

Conditions for (mod 1) uniform distribution are altered by perturbations

Classical uniform distribution criteria are not directly applicable in perturbed settings

Abstract

We examine the uniform distribution theory of H. Weyl when there is a periodic perturbation present. As opposed to the classical setting, in this case the conditions for (mod 1) density and (mod 1) uniform distribution turn out to be different.