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On weighted inhomogeneous Diophantine approximation on planar curves

Published online by Cambridge University Press:  01 October 2012

MUMTAZ HUSSAIN  and
TATIANA YUSUPOVA
MUMTAZ HUSSAIN
Affiliation:
Department of Mathematics and Statistics, La Trobe University, Melbourne, 3086, Victoria, Australia. e-mail: m.hussain@latrobe.edu.au
TATIANA YUSUPOVA
Affiliation:
Department of Mathematics, University of York, Heslington, York, YO10, 5DD. e-mail: tatiana.yusupova@gmail.com
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Abstract

This paper develops the metric theory of simultaneous inhomogeneous Diophantine approximation on a planar curve with respect to multiple approximating functions. Our results naturally generalize the homogeneous Lebesgue measure and Hausdorff dimension results for the sets of simultaneously well-approximable points on planar curves, established in Badziahin and Levesley (Glasg. Math. J., 49(2):367–375, 2007), Beresnevich et al. (Ann. of Math. (2), 166(2):367–426, 2007), Beresnevich and Velani (Math. Ann., 337(4):769–796, 2007) and Vaughan and Velani (Invent. Math., 166(1):103–124, 2006).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 154 , Issue 2 , March 2013 , pp. 225 - 241
Copyright
Copyright © Cambridge Philosophical Society 2012

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References

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