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An Inhomogeneous Jarník type theorem for planar curves

Badziahin, D.; Harrap, S.; Hussain, M.

An Inhomogeneous Jarník type theorem for planar curves Thumbnail


Authors

D. Badziahin

M. Hussain



Abstract

In metric Diophantine approximation there are classically four main classes of approximations: simultaneous and dual for both homogeneous and inhomogeneous settings. The well known measure-theoretic theorems of Khintchine and Jarník are fundamental to each of them. Recently, there has been substantial progress towards establishing a metric theory of Diophantine approximation on manifolds for each of the classes above. In particular, both Khintchine and Jarník-type results have been established for approximation on planar curves except for only one case. In this paper, we prove an inhomogeneous Jarník type theorem for convergence on planar curves in the setting of dual approximation and in so doing complete the metric theory of Diophantine approximation on planar curves.

Citation

Badziahin, D., Harrap, S., & Hussain, M. (2017). An Inhomogeneous Jarník type theorem for planar curves. Mathematical Proceedings of the Cambridge Philosophical Society, 163(1), 47-70. https://doi.org/10.1017/s0305004116000712

Journal Article Type Article
Online Publication Date Sep 9, 2016
Publication Date Jul 1, 2017
Deposit Date Dec 30, 2015
Publicly Available Date Mar 9, 2017
Journal Mathematical Proceedings of the Cambridge Philosophical Society
Print ISSN 0305-0041
Electronic ISSN 1469-8064
Publisher Cambridge University Press
Peer Reviewed Peer Reviewed
Volume 163
Issue 1
Pages 47-70
DOI https://doi.org/10.1017/s0305004116000712
Public URL https://durham-repository.worktribe.com/output/1416057
Related Public URLs http://arxiv.org/abs/1503.04981

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Copyright Statement
This article has been published in a revised form in Mathematical proceedings of the Cambridge Philosophical Society https://doi.org/10.1017/S0305004116000712. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © Cambridge Philosophical Society 2016





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