caa a22 4500 386307253 CHVBK 20180307111533.0 cr unu---uuuuu 161130e198810 xx s 000 0 eng 10.1017/S1446788700030159 doi S1446788700030159 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700030159 Some quantitative results related to Roth's Theorem [Elektronische Daten] 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. Copyright © Australian Mathematical Society 1988 11 J 68 nationallicence Bombieri E. School of Mathematics, The Institute for Advanced Study Princeton, New Jersey 08540, U.S.A. van der Poorten A. J. School of Mathematics and Physics, Macquarie University N.S.W. 2109, Australia Journal of the Australian Mathematical Society Cambridge University Press 45/2(1988-10), 233-248 1446-7887 45:2<233 1988 45 JAZ https://doi.org/10.1017/S1446788700030159 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700030159 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bombieri E. School of Mathematics, The Institute for Advanced Study Princeton, New Jersey 08540, U.S.A NATIONALLICENCE 700 1- van der Poorten A. J. School of Mathematics and Physics, Macquarie University N.S.W. 2109, Australia NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 45/2(1988-10), 233-248 1446-7887 45:2<233 1988 45 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence SWISSBIB 386307253 BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge