Some quantitative results related to Roth's theorem

E. Bombieri, A. J. Van Der Poorten

Research output: Contribution to journalArticlepeer-review

20 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 languageEnglish
Pages (from-to)233-248
Number of pages16
JournalJournal of the Australian Mathematical Society
Volume45
Issue number2
DOIs
Publication statusPublished - 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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