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Hall's ray in inhomogeneous diophantine approximation

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  09 April 2009

T. W. Cusick ,
W. Moran  and
A. D. Pollington
T. W. Cusick
Affiliation:
Department of MathematicsSUNY at BuffaloNY 14214-3093USA
W. Moran
Affiliation:
School of Information Science and TechnologyFlinders UniversityGPO 2100, SA5001Australia
A. D. Pollington
Affiliation:
Department of MathematicsBrigham Young UniversityProvo, UT 84602USA
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Abstract

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The aim of the paper is to show the existence of a ‘Hall's ray’ for the particular case of the one-sided inhomogeneous diophantine approximation problem, where the irrational is the golden ratio. The proof uses a sum-set method similar to that used by Marshall Hall for the original result of this kind.

MSC classification

Secondary: 11J06: Markov and Lagrange spectra and generalizations 11J20: Inhomogeneous linear forms
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 60 , Issue 1 , February 1996 , pp. 42 - 50
Copyright
Copyright © Australian Mathematical Society 1996

References

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