Revision of van der Corput lemma for equidistribution from Mon, 20/04/2009 - 23:32

This means that it cannot be considered to contain or lead to any mathematically interesting information.

Quick description

If $x_n$ is a sequence mod 1, such that $x_{n+h} - x_n$ is uniformly distributed modulo 1 for all non-zero h, then $x_n$ is also uniformly distributed modulo 1.

Prerequisites

Undergraduate analysis

Example 1

(Equidistribution of polynomials)

Example 2

(Multiple recurrence in weakly mixing systems)

General discussion

A quantitative version of this fact, known as van der Corput's inequality, is also useful.

(Also mention Bergelson's Hilbert space version.)

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