An effective version of the Lindemann-Weierstrass theorem for interpolation determinants
type: Item
instance of: scholarly article
title: An effective version of the Lindemann-Weierstrass theorem for interpolation determinants
zbMATH Open document ID: 0935.11024
author: Alain Sert
published in: Journal of Number Theory
publication date: 2000-05-11T00:00:00Z
review text: The best known quantitative version of the Lindemann-Weierstrass theorem was given by \textit{M. Ably} [Acta Arith. 67, 29-45 (1994; Zbl 0813.11042)] by using Philippon's criterion for algebraic independence. Here the author uses Laurent's interpolation determinants to obtain a lower bound of the same type for \(|P(e^{\alpha_1},\dots, e^{\alpha_p})|\) where the \(\alpha_j\) are complex algebraic numbers, linearly independent over \(\mathbb{Q}\), and \(P\) is a polynomial with algebraic coefficients. In comparison with Ably's result (where \(P\) has rational coefficients) this bound is a little better for the dependence on \(P\) and especially entirely explicit for the dependence on the \(\alpha_j\). This paper is a very nice piece of virtuosity.
Mathematics Subject Classification ID: 11J85
Mathematics Subject Classification ID: 11J82
zbMATH DE Number: 1310086
zbMATH Keywords: measure of algebraic independence
zbMATH Keywords: Lindemann-Weierstrass theores
reviewed by: François Gramain
MaRDI profile type: Publication
full work available at URL: jnth.1998.2356
OpenAlex ID: W1999238597
cites work: Une version quantitative du théorème de Lindemann-Weierstrass
cites work: On Siegel's lemma
cites work: Linear forms in two logarithms and interpolation determinants
DOI: 10.1006/JNTH.1998.2356
description: scientific article; zbMATH DE number 1310086