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Best Diophantine approximations to a set of linear forms

Published online by Cambridge University Press:  09 April 2009

J. C. Lagarias
J. C. Lagarias
Affiliation:
Bell Laboratories Murray Hill, New Jersey 07974, U.S.A.
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Abstract

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We define the notion of a best Diophantine approximation vector to a set of linear forms. This generalizes definitions of a best approximation vector to a single linear form and of a best simultaneous Diophantine approximation vector. We derive necessary and sufficient conditions for the existence of an infinite set of best Diophantine approximation vectors. Finally, we prove that such approximation vectors are spaced far apart in an appropriate sense.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 34 , Issue 1 , February 1983 , pp. 114 - 122
Copyright
Copyright © Australian Mathematical Society 1983

References

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