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Continued fractions with low complexity: transcendence measures and quadratic approximation

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  19 March 2012

Yann Bugeaud
Yann Bugeaud*
Affiliation:
Mathématiques, Université de Strasbourg, 7, rue René Descartes, 67084 Strasbourg, France (email: bugeaud@math.unistra.fr)
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Abstract

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We establish measures of non-quadraticity and transcendence measures for real numbers whose sequence of partial quotients has sublinear block complexity. The main new ingredient is an improvement of Liouville’s inequality giving a lower bound for the distance between two distinct quadratic real numbers. Furthermore, we discuss the gap between Mahler’s exponent w2 and Koksma’s exponent w*2.

Keywords

continued fractiontranscendenceSchmidt’s subspace theorem

MSC classification

Secondary: 11J70: Continued fractions and generalizations 11J82: Measures of irrationality and of transcendence 11J87: Schmidt Subspace Theorem and applications
Type
Research Article
Information
Compositio Mathematica , Volume 148 , Issue 3 , May 2012 , pp. 718 - 750
Copyright
Copyright © Foundation Compositio Mathematica 2012

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