A note on badly approximable systems of linear forms over a field of formal series

A note on badly approximable systems of linear forms over a field of formal series

We prove that the set of badly approximable systems of M linear forms in N variables over the field of formal power series is hyperplane absolute winning. A consequence of this winning property is that the set has full Hausdorff dimension.

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Research in number theory 2023-06, Vol.9 (2), Article 31
Hauptverfasser: Hussain, Mumtaz, Shulga, Nikita
Format: Artikel
Sprache:eng
Schlagworte:
Hyperplanes
Mathematics
Mathematics and Statistics
Number Theory
Power series
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We prove that the set of badly approximable systems of M linear forms in N variables over the field of formal power series is hyperplane absolute winning. A consequence of this winning property is that the set has full Hausdorff dimension.
ISSN:2522-0160
2363-9555
DOI:10.1007/s40993-023-00437-x