On rational approximations to linear forms in values of \(G\)-functions
type: Item
instance of: scholarly article
title: On rational approximations to linear forms in values of \(G\)-functions
zbMATH Open document ID: 0814.11038
author: M. Nagata
published in: Proceedings of the Japan Academy. Series A
publication date: 1994-08-08T00:00:00Z
full work available at URL: https://eudml.org/doc/206754
review text: The author announces (detailed proofs will appear elsewhere) results on linear independence measures of the values of \(G\)-functions. Lower bounds are given in terms of all the coefficients of the linear form and the results generalize the earlier work of the reviewer [Acta Arith. 36, 273- 295 (1980; Zbl 0369.10021)], where the ideas of \textit{A. Baker} [Can. J. Math. 17, 616-626 (1965; Zbl 0147.309)] combined with Siegel-Shidlovskij theory were used to estimate linear independence measures of the values of \(G\)-functions satisfying Galochkin's \((G,C)\)-condition. The fact that \(G\)-functions satisfy the \((G,C)\)-condition was proved in the important work of \textit{G. V.} and \textit{D. V. Chudnovsky} [Lect. Notes Math. 1135, 9-51 (1985; Zbl 0561.10016)], where also some results of the type of the present work were announced.
Mathematics Subject Classification ID: 11J91
Mathematics Subject Classification ID: 11J82
zbMATH DE Number: 597324
zbMATH Keywords: irrationality measure
zbMATH Keywords: values of \(G\)-functions
zbMATH Keywords: linear independence measures
zbMATH Keywords: Galochkin's \((G,C)\)-condition
MaRDI profile type: Publication
OpenAlex ID: W2074561362
cites work: Q3994840
cites work: Q3998726
cites work: Q3910600
cites work: Q5184974
cites work: On some applications of diophantine approximations
cites work: ESTIMATES FROM BELOW OF POLYNOMIALS IN THE VALUES OF ANALYTIC FUNCTIONS OF A CERTAIN CLASS
cites work: Transcendental numbers. With a foreword by W. Dale Brownawell. Transl. from the Russian by Neal Koblitz
cites work: On linear forms of a certain class of G-functions and p-adic G-functions
DOI: 10.3792/PJAA.70.27
description: scientific article; zbMATH DE number 597324