Abstract
We show an analog of a theorem of [J. An, A. Ghosh, L. Guan and T. Ly, Bounded orbits of diagonalizable flows on finite volume quotients of products of [Formula: see text], Adv. Math. 354 (2019) 106743] on weighted badly approximable vectors for totally imaginary number fields. We show that for [Formula: see text] and [Formula: see text] a lattice subgroup, the points of [Formula: see text] with bounded orbits under a one-parameter Ad-semisimple subgroup of [Formula: see text] form a hyperplane-absolute-winning set. As an application, we also provide a generalization of a result of [R. Esdahl-Schou and S. Kristensen, On badly approximable complex numbers, Glasgow Math. J. 52 (2010) 349–355] about the set of badly approximable complex numbers.
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.
