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A NOTE ON BADLY APPROXIMABLE LINEAR FORMS

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  04 February 2011

MUMTAZ HUSSAIN
MUMTAZ HUSSAIN*
Affiliation:
Department of Mathematics and Statistics, La Trobe University, Melbourne, Victoria 3086, Australia (email: m.hussain@latrobe.edu.au)
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Abstract

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In this paper we investigate the analogue of the classical badly approximable setup in which the distance to the nearest integer ‖⋅‖ is replaced by the sup norm |⋅|. In the case of one linear form we prove that the hybrid badly approximable set is of full Hausdorff dimension.

Keywords

Diophantine approximationsystems of linear formsHausdorff dimension

MSC classification

Secondary: 11J25: Diophantine inequalities
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 83 , Issue 2 , April 2011 , pp. 262 - 266
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

References

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