A Jarník type theorem for planar curves: everything about the parabola

Title: A Jarník type theorem for planar curves: everything about the parabola
Creator: Hussain, Mumtaz
Relation: Mathematical proceedings of the Cambridge Philosophical Society Vol. 159, Issue 1, p. 47-60
Publisher Link: http://dx.doi.org/10.1017/S0305004115000195
Publisher: Cambridge Philosophical Society
Resource Type: journal article
Date: 2015
Description: The well-known theorems of Khintchine and Jarník in metric Diophantine approximation provide a comprehensive description of the measure theoretic properties of real numbers approximable by rational numbers with a given error. Various generalisations of these fundamental results have been obtained for other settings, in particular, for curves and more generally manifolds. In this paper we develop the theory for planar curves by completing the theory in the case of parabola. This represents the first comprehensive study of its kind in the theory of Diophantine approximation on manifolds.
Subject: Khintchine theorem; Jarnik theorem; real numbers; Diophantine approximation
Identifier: http://hdl.handle.net/1959.13/1321438
Identifier: uon:24362
Identifier: ISSN:0305-0041
Language: eng
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