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Restricted diophantine approximation

Published online by Cambridge University Press:  09 April 2009

R. T. Worley
R. T. Worley
Affiliation:
Department of Mathematics, Monash University, Victoria 3168, Australia.
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Abstract

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The problem considered is that of approximating irrationals α by rationals p/q where p and q avoid certain congruence classes mod 2k for certain integers k. Results are obtained which give close bounds on a number c such that |α - p/q| < c/q2 has infinitely many solutions where p and q can be expressed as the sum of three squares.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 24 , Issue 4 , December 1977 , pp. 425 - 439
Copyright
Copyright © Australian Mathematical Society 1977

References

Scott, W. T. (1940), ‘Approximations to real irrationals by certain classes of rational fractions’, Bull. Am. Math. Soc. 46 124–29.Google Scholar
Lekkerkerker, C. A. (1969), Geometry of Numbers, Walters Nordhoff.Google Scholar
Lang, S. (1966), Introduction to diophantine approximation, Addison Wesley.Google Scholar