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

Hussain, Mumtaz; Shulga, Nikita

doi:10.26181/22639777.v1

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

journal contribution

posted on 2023-04-17, 05:39 authored by Mumtaz HussainMumtaz Hussain, Nikita ShulgaNikita Shulga

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.

History

Publication Date

2023-06-01

Journal

Research in Number Theory

Volume

9

Issue

2

Article Number

31

Pagination

13p.

Publisher

Springer Nature

ISSN

2522-0160

Rights Statement

© The Author(s) 2023. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.