Ideal constructions and irrationality measures of roots of algebraic numbers

Paula B. Cohen*, Alfred J. Van Der Poorten

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)63-80
Number of pages18
JournalIllinois Journal of Mathematics
Issue number1
Publication statusPublished - Mar 2002


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