An inhomogeneous Jarník type theorem for planar curves

Title: An inhomogeneous Jarník type theorem for planar curves
Creator: Badziahin, Dzmitry; Harrap, Stephen; Hussain, Mumtaz
Relation: Mathematical Proceedings of the Cambridge Philosophical Society Vol. 163, Issue 1, p. 47-70
Publisher Link: http://dx.doi.org/10.1017/S0305004116000712
Publisher: Cambridge University Press
Resource Type: journal article
Date: 2017
Description: 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.
Subject: approximations; Jarník; Jarník -type theorem; planar curves
Identifier: http://hdl.handle.net/1959.13/1391745
Identifier: uon:33285
Identifier: ISSN:0305-0041
Language: eng
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