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INTRINSIC DIOPHANTINE APPROXIMATION ON GENERAL POLYNOMIAL SURFACES

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  02 November 2016

Morten Hein Tiljeset
Morten Hein Tiljeset*
Affiliation:
Department of Mathematical Sciences, Faculty of Science, University of Aarhus, Ny Munkegade 118, DK-8000 Aarhus C, Denmark email [email protected]
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Abstract

We study the Hausdorff measure and dimension of the set of intrinsically simultaneously $\unicode[STIX]{x1D713}$-approximable points on a curve, surface, etc, given as a graph of integer polynomials. We obtain complete answers to these questions for algebraically “nice” manifolds. This generalizes earlier work done in the case of curves.

MSC classification

Primary: 11J83: Metric theory
Secondary: 11J54: Small fractional parts of polynomials and generalizations
Type
Research Article
Information
Mathematika , Volume 63 , Issue 1 , 2017 , pp. 250 - 259
Copyright
Copyright © University College London 2016 

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