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An inhomogeneous Jarník type theorem for planar curves.

Badziahin, D. and Harrap, S. and Hussain, M. (2017) 'An inhomogeneous Jarník type theorem for planar curves.', Mathematical proceedings of the Cambridge Philosophical Society., 163 (1). pp. 47-70.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1017/S0305004116000712
Publisher 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
Date accepted:No date available
Date deposited:14 December 2016
Date of first online publication:09 September 2016
Date first made open access:14 December 2016

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