On the linear independence in algebraic number fields
type: Item
instance of: scholarly article
title: On the linear independence in algebraic number fields
zbMATH Open document ID: 0804.11045
DOI: 10.1007/BF03323148
author: Thomas Töpfer
published in: Results in Mathematics
publication date: 1994-05-31T00:00:00Z
review text: In a recent work of \textit{P. Bundschuh} and the author [Monatsh. Math. 117, 17-32 (1994; see the review above)] obtained a criterion of linear independence over \(\mathbb{Q}\) by generalizing the earlier linear independence considerations of \textit{Yu. V. Nesterenko} [Vestn. Mosk. Univ., Ser. I 1985, No. 1, 46-49 (1985; Zbl 0572.10027)]. In the present paper the author introduces a further development of the method for the consideration of criteria of linear independence over arbitrary algebraic number fields. The results are given also in the quantitative form and as an application an explicit quantitative version of the Lindemann- Weierstrass theorem is proved, see also a paper of \textit{M. Ably} [Acta Arith. 67, No. 1, 29-45 (1994)], where the Lindemann-Weierstrass theorem is considered by another method.
Mathematics Subject Classification ID: 11J82
Mathematics Subject Classification ID: 11J72
zbMATH DE Number: 554055
zbMATH Keywords: linear independence over arbitrary algebraic number fields
zbMATH Keywords: explicit quantitative version of the Lindemann-Weierstrass theorem
MaRDI profile type: Publication
cites work: Q4697140
cites work: On Some Diophantine Inequalities Involving the Exponential Function
cites work: Einführung in die Zahlentheorie
cites work: On linear independence
cites work: THE DEVELOPMENT AND PRESENT STATE OF THE THEORY OF TRANSCENDENTAL NUMBERS
cites work: Q5542232
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full work available at URL: https://doi.org/10.1007/bf03323148
OpenAlex ID: W2168084087
description: scientific article; zbMATH DE number 554055