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Metrical properties of best approximants

Part of: Diophantine approximation, transcendental number theory Probabilistic theory: distribution modulo $1$; metric theory of algorithms

Published online by Cambridge University Press:  09 April 2009

Jos Blom
Jos Blom
Affiliation:
Harrelaers 11 1852 KT, Heiloo The, Netherlands
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Abstract

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A rational number is called a best approximant of the irrational number ζ if it lies closer to ζ than all rational numbers with a smaller denominator. Metrical properties of these best approximants are studied. The main tool is the two-dimensional ergodic system, underlying the continued fraction expansion.

MSC classification

Secondary: 11J70: Continued fractions and generalizations 11K50: Metric theory of continued fractions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 53 , Issue 1 , August 1992 , pp. 78 - 91
Copyright
Copyright © Australian Mathematical Society 1992

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