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Some quantitative results related to Roth's Theorem

Part of: Diophantine approximation, transcendental number theory

Published online by Cambridge University Press:  09 April 2009

E. Bombieri  and
A. J. van der Poorten
E. Bombieri
Affiliation:
School of Mathematics, The Institute for Advanced Study Princeton, New Jersey 08540, U.S.A.
A. J. van der Poorten
Affiliation:
School of Mathematics and Physics, Macquarie UniversityN.S.W. 2109, Australia
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Abstract

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We employ the Dyson's Lemma of Esnault and Viehweg to obtain a new and sharp formulation of Roth's Theorem on the approximation of algebraic numbers by algebraic numbers and apply our arguments to yield a refinement of the Davenport-Roth result on the number of exceptions to Roth's inequality and a sharpening of the Cugiani-Mahler theorem. We improve on the order of magnitude of the results rather than just on the constants involved.

MSC classification

Secondary: 11J68: Approximation to algebraic numbers
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 45 , Issue 2 , October 1988 , pp. 233 - 248
Copyright
Copyright © Australian Mathematical Society 1988

References

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