Diophantine approximation by conjugate algebraic integers
| dc.creator | Roy, Damien | |
| dc.creator | Waldschmidt, Michel | |
| dc.date | 2002-07-12 | |
| dc.date | 2003-06-04 | |
| dc.date.accessioned | 2026-07-07T04:49:39Z | |
| dc.date.available | 2026-07-07T04:49:39Z | |
| dc.description | Building on 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 $ξ$ to be algebraic in terms of the existence of polynomials of bounded degree taking small values at $ξ$ together with most of their derivatives. The second one, which follows from this criterion by an argument of duality, is a result of simultaneous approximation by conjugate algebraic integers for a fixed number $ξ$ that is either transcendental or algebraic of sufficiently large degree. We also present several constructions showing that these results are essentially optimal. | |
| dc.description | 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 | |
| dc.identifier | https://arxiv.org/abs/math/0207102 | |
| dc.identifier | http://arxiv.org/abs/math/0207102 | |
| dc.identifier | Compositio Math. 140 (2004), 593--612. | |
| dc.identifier | doi:10.1112/S0010437X03000708 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64500 | |
| dc.subject | Number Theory | |
| dc.subject | 11J13 | |
| dc.title | Diophantine approximation by conjugate algebraic integers | |
| dc.type | text |