A zero lemma
type: Item
instance of: scholarly article
title: A zero lemma
zbMATH Open document ID: 1031.11046
DOI: 10.1016/S1631-073X(02)02422-6
author: Nicolas Gouillon
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2002-11-24T00:00:00Z
review text: In 1981 \textit{D. W.~Masser} [Invent. Math. {63}, 81-95 (1981; Zbl 0436.32005)] proved a zero estimate for exponential polynomials in several variables which had a number of applications to transcendental number theory. This estimate was refined by several authors; especially \textit{P.~Philippon} [Bull. Soc. Math. Fr. {114}, 355-383 (1986; Zbl 0617.14001); Errata et addenda, ibid. {115}, 397-398 (1987; Zbl 0634.14001); Rocky Mt. J. Math. 26, 1069-1088 (1996; Zbl 0893.11027)]. Here the author introduces a further improvement which sharpens Philippon's results. The refinement arises from the fact that in the proof, the conditions he checks are not the same for each step. The main condition is the same, but the other ones are essentially less restrictive. In another work the author uses his zero estimate to derive sharp linear independence measures for two logarithms of algebraic numbers.
reviewed by: Michel Waldschmidt
Mathematics Subject Classification ID: 11J95
Mathematics Subject Classification ID: 11J81
Mathematics Subject Classification ID: 32A60
Mathematics Subject Classification ID: 14A05
Mathematics Subject Classification ID: 14C17
Mathematics Subject Classification ID: 14L10
Mathematics Subject Classification ID: 33B10
Mathematics Subject Classification ID: 11J86
zbMATH DE Number: 1803921
zbMATH Keywords: Zero estimate
zbMATH Keywords: linear forms in logarithms
MaRDI profile type: Publication
cites work: On polynomials and exponential polynomials in several complex variables
cites work: Lemmes de zéros dans les groupes algébriques commutatifs
description: scientific article; zbMATH DE number 1803921