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Simultaneous Diophantine approximation

Published online by Cambridge University Press:  09 April 2009

J. M. Mack
J. M. Mack
Affiliation:
Department of Pure Mathematics, University of Sydney, N.S.W. 2006, Australia.
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Abstract

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Using a method suggested by E. S. Barnes, it is shown that the simultaneous inequalities r(p — αr)2 < c, r(q — βr)2 < c have an infinity of integral solutions p, q, r (with r > 0), for arbitrary irrationals α and β, provided that c > 1/2.6394. This improves an earlier result of Davenport, who shows that the same conclusion holds if c > 1/46¼ = 1/2.6043 ….

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 24 , Issue 3 , November 1977 , pp. 266 - 285
Copyright
Copyright © Australian Mathematical Society 1977

References

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