2002/07/31 by Damien Roy, Michel Waldschmidt
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Algebraic Geometry and Number Theory #Mathematical Dynamics and Fractals #math.NT #msc:11J13
paper · pdf · doi:10.1112/s0010437x03000708
published as Compositio Math. 140 (2004), 593--612. · The section 4 of this new version has been rewritten to simplify the proof of the main result. Other results in Sections 9 and 10 have been improved. To appear in Compositio Math
arxiv created 2003/06/04 · openalex publication_date 2004/04/14 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Building on the work of Davenport and Schmidt, we mainly prove two results. The first one is a version of Gel'fond's transcendence criterion which provides a sufficient condition for a complex or p-adic number that is either transcendental or algebraic of sufficiently large degree. We also present several constructions showing that these results are essentially optimal.