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On badly approximable numbers

Published online by Cambridge University Press:  26 February 2010

Wolfgang M. Schmidt
Wolfgang M. Schmidt
Affiliation:
University of Colorado, Boulder, U.S.A.
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Extract

Write ‖θ‖ for the distance from the real number θ to the nearest integer. An n-tuple of real numbers (β1, …, βn) will be called badly approximable, if there is constant C > 0 such that

for all positive integers q. As is well known, a single number β is badly approximable if and only if the partial quotients in its continued fraction are bounded.

Type
Research Article
Information
Mathematika , Volume 12 , Issue 1 , June 1965 , pp. 10 - 20
Copyright
Copyright © University College London 1965

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References

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