Dispersion and Littlewood's conjecture

Let ε>0. We construct an explicit, full-measure set of α∈[0,1] such that if γ∈R then, for almost all β∈[0,1], if δ∈R then there are infinitely many integers n⩾1 for whichn‖nα−γ‖⋅‖nβ−δ‖

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2024-06, Vol.447, p.109697, Article 109697
Main Authors: Chow, Sam, Technau, Niclas
Format: Article
Language:English
Subjects:
Diophantine approximation
Lacunary sequences
Rajchman measures
Uniform distribution
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Description
Summary:Let ε>0. We construct an explicit, full-measure set of α∈[0,1] such that if γ∈R then, for almost all β∈[0,1], if δ∈R then there are infinitely many integers n⩾1 for whichn‖nα−γ‖⋅‖nβ−δ‖
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2024.109697