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Applications of Padé approximations to diophantine inequalities in values of G-functions. (English) Zbl 0561.10016

Number theory, Semin. New York 1983-84, Lect. Notes Math. 1135, 9-51 (1985).
[For the entire collection see Zbl 0553.00003.]
Several papers by K. Väänänen, V. G. Sprindzhuk, E. Bombieri, P. Dèbes, the authors,...) have been published recently, dealing with Siegel’s G-functions. Usually, their proofs involve an auxiliary function which is related to Padé approximants of the first kind. Here the authors rely on Padé approximants of the second kind. They prove several general results on G-functions satisfying a system of first order linear differential equations with algebraic coefficients, without assuming that the functions are what some authors call (G,C)-functions. In fact one of the results here is that this (G,C)-condition is always fulfilled by such linearly independent functions. Finally the authors mention a consequence of their results to Thue equation.
Reviewer: M.Waldschmidt

MSC:

11J81 Transcendence (general theory)
41A21 Padé approximation
11D57 Multiplicative and norm form equations
11D61 Exponential Diophantine equations

Citations:

Zbl 0553.00003