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One-dimensional quasi-uniform Kronecker sequences
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Journal Article
One-dimensional quasi-uniform Kronecker sequences
2024
Overview
In this short note, we prove that the one-dimensional Kronecker sequence
i
α
mod
1
,
i
=
0
,
1
,
2
,
…
,
is quasi-uniform over the unit interval [0, 1] if and only if
α
is a badly approximable number. Our elementary proof relies on a result on the three-gap theorem for Kronecker sequences due to Halton (Proc Camb Philos Soc, 61:665–670, 1965).
Publisher
Springer International Publishing,Springer Nature B.V
