A note on badly approximable systems of linear forms over a field of formal series-Reference-Cited by-同舟云学术

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

Published:2023-04-15 Issue:2 Volume:9 Page:
ISSN:2522-0160
Container-title:Research in Number Theory
language:en
Short-container-title:Res. number theory

Author:

Hussain Mumtaz^ORCID,Shulga Nikita

Abstract

AbstractWe 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.

Funder

Australian Research Council

Publisher

Springer Science and Business Media LLC

Subject

Algebra and Number Theory

Link

https://link.springer.com/content/pdf/10.1007/s40993-023-00437-x.pdf

Reference13 articles.

1. Badziahin, D., Harrap, S.: Cantor-winning sets and their applications. Adv. Math. 318, 627–677 (2017)

2. Broderick, R., Fishman, L., Kleinbock, D., Reich, A., Weiss, B.: The set of badly approximable vectors is strongly $$C^1$$ incompressible. Math. Proc. Cambridge Philos. Soc. 153(02), 319–339 (2012)

3. Broderick, R., Fishman, L., Simmons, D.: Badly approximable systems of affine forms and incompressibility on fractals. J. Number Theory 133(7), 2186–2205 (2013)

4. Fishman, L., Simmons, D., Urbański, M.: Diophantine approximation and the geometry of limit sets in Gromov hyperbolic metric spaces. Mem. Am. Math. Soc. 254(1215), v+137, (2018)

5. Hussain, M., Kristensen, S., Simmons, D.: Metrical theorems on systems of affine forms. J. Number Theory 213, 67–100 (2020)

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