### Quick description

If is a sequence mod 1, such that is uniformly distributed modulo 1 for all non-zero h, then 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.)

Not to be confused with the van der Corput lemma for oscillatory integrals.

5 years 3 weeksago5 years 12 weeksago5 years 13 weeksago5 years 42 weeksago6 years 11 weeksago