Abstract
This paper addresses the problem of determining the best results one can expect using the Thue-Siegel method as developed by Bombieri in his equivariant approach to effective irrationality measures to roots of high order of algebraic numbers, in the non-archimedean setting. As an application, we show that this method, under a non-vanishing assumption for the auxiliary polynomial which replaces the appeal to Dyson's Lemma type arguments and together with a version of Siegel's Lemma due to Struppeck and Vaaler, yields a result comparable to the best results obtained to date by transcendence methods.
Citation
Paula B. Cohen. Alfred J. van der Poorten. "Ideal construction and irrationality measures of roots of algebraic numbers." Illinois J. Math. 46 (1) 63 - 80, Spring 2002. https://doi.org/10.1215/ijm/1258136140
Information