On rational approximations to linear forms in values of \(G\)-functions (Q1327769)

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.