J Austral Math Soc Ser A 45 pp233--248, 1988.

Some Quantitative Results Related to Roth's Theorem

E. Bombieri and A. J. van der Poorten

Abstract

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 exeptions 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.

1980 AMS Subject Classification: 11J68

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Authors

E. Bombieri

School of Mathematics, The Institute for Advanced Study, Princeton, New Jersey 08540, U.S.A.

A. J. van der Poorten

School of Mathematics and Physics, Macquarie University, N.S.W. 2109, Australia.