Some quantitative results related to Roth's theorem

E. Bombieri; A. J. Van Der Poorten

doi:10.1017/S1446788700030159

Some quantitative results related to Roth's theorem

E. Bombieri, A. J. Van Der Poorten

Macquarie University Administration Unit

Research output: Contribution to journal › Article › peer-review

23 Citations (Scopus)

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 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.

Original language	English
Pages (from-to)	233-248
Number of pages	16
Journal	Journal of the Australian Mathematical Society
Volume	45
Issue number	2
DOIs	https://doi.org/10.1017/S1446788700030159
Publication status	Published - 1988

Bibliographical note

Corrigendum can be found in Journal of the Australian Mathematical Society, 48(1), pp. 154-155, 1990.
https://doi.org/10.1017/S1446788700035291

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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 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.",

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N2 - 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.

AB - 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.

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Some quantitative results related to Roth's theorem

Abstract

Bibliographical note

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