Abstract
We prove that for any s, t ⩾ 0 with s + t = 1 and any θ ∈ ℝ with infq∈ℕq1/s||qθ|| > 0, the set of y ∈ ℝ for which (θ, y) is (s, t)-badly approximable is ½-winning for Schmidt's game. As a consequence, we remove a technical assumption in a recent theorem of Badziahin–Pollington–Velani on simultaneous Diophantine approximation.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
