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SIMULTANEOUS DIOPHANTINE APPROXIMATION ON POLYNOMIAL CURVES

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  10 December 2009

Natalia Budarina ,
Detta Dickinson  and
Jason Levesley
Natalia Budarina
Affiliation:
Department of Mathematics, Logic House, NUI Maynooth, Co Kildare, Republic of Ireland
Detta Dickinson
Affiliation:
Department of Mathematics, Logic House, NUI Maynooth, Co Kildare, Republic of Ireland (email: ddickinson@maths.nuim.ie)
Jason Levesley
Affiliation:
Department of Mathematics, University of York, Heslington, York YO10 5DD, U.K.
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Abstract

The Hausdorff dimension and measure of the set of simultaneously ψ-approximable points lying on integer polynomial curves is obtained for sufficiently small error functions.

MSC classification

Secondary: 11J13: Simultaneous homogeneous approximation, linear forms 11J83: Metric theory 11J54: Small fractional parts of polynomials and generalizations

Information

Type
Research Article
Information
Mathematika , Volume 56 , Issue 1 , January 2010 , pp. 77 - 85
Copyright
Copyright © University College London 2010

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