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 |
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Pages (from-to) | 233-248 |
Number of pages | 16 |
Journal | Journal of the Australian Mathematical Society |
Volume | 45 |
Issue number | 2 |
DOIs | |
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