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References
C.L. Siegel, Über einige Anwendungen diophantischer Approximationen, Abh. Preuss. Akad. Wiss. Phys. Math. Kl. 1, 1929.
C.L. Siegel, Transcendental Numbers, Princeton University Press, Princeton, 1949.
G.V. Chudnovsky, Contributions to the Theory of Transcendental Numbers, Mathematical Surveys and Monographs, 19, American Mathematical Society, 1984, Chapter 5.
D.V. Chudnovsky, G.V. Chudnovsky, Applications of Padé approximations to the Grothendieck conjecture on linear differential equations, see next paper, this volume.
A. Baker, Transcendental Number Theory, Cambridge University Press, Cambridge, 1979.
A.L. Galočhkin, Lower bounds of polynomials in the values of a certain class of analytic functions, Math. Sb. 95 (1974), 396–417.
K. Väänänen, On linear forms of certain class of G-functions and p-adic G-functions, Acta Arith. 36 (1980), 273–295.
Y.Z. Flicker, On p-adic G-functions, J. London Math. Soc. 15 (1977), 395–402.
E. Bombieri, On G-functions, in Recent Progress in Analytic Number Theory (ed. by H. Halberstam and C. Hooly), Academic Press, N.Y., v.2, 1981, 1–67.
G.V. Chudnovsky, Measures of irrationality, transcendence and algebraic independence.Recent progress, in Journees Arithmetiques 1980 (ed. by J.V. Armitage), Cambridge University Press, 1982, 11–82.
N. Katz, Algebraic solutions of differential equations, Invent. Math., 18 (1972), 1–118.
T. Honda, Algebraic differential equations, Symposia Mathematica v. 24, Academic Press, N.Y., 1981, 169–204.
B. Dwork, Arithmetic theory of differential equations, ibid., 225–243.
K. Mahler, Perfect systems, Composito Math. 19 (1968), 95–166.
K. Mahler, An analogue to Minkowski's geometry of numbers in a field of series, Ann. of Math. 42 (1941), 488–522.
W.M. Schmidt, Diophantine Approximations, Lecture Notes Math. v. 785, Springer, 1980.
E.R. Kolchin, Rational approximations to solutions of algebraic differential equations, Proc. Amer. Math. Soc. 10 (1959), 238–244.
D.V. Chudnovsky, G.V. Chudnovsky, Rational approximations to solutions of linear differential equations, Proc. Nat'l. Acad. Sci. USA 80 (1983), 5158–5162.
D.V. Chudnovsky, G.V. Chudnovsky, Padé approximations to solutions of linear differential equations and applications to diophantine analysis, Lecture Notes Math. v. 1052, Springer, 1984, 85–167.
G.V. Chudnovsky, On some applications of diophantine approximations, Proc. Nat'l. Acad. Sci. USA 81 (1984), 1926–1930.
J.W.S. Cassels, An Introduction to Diophantine Approximations, Cambridge University Press, Cambridge, 1957.
J. Nuttal, Asymptotics of diagonal Hermite-Padé polynomials, J. Approximation Theory, 1985 (in press).
C. Brezinski, Padé-type Approximations and General Orthogonal Polynomials, Birkhauser, Boston, 1980.
G.V. Chudnovsky, The Thue-Siegel-Roth theorem for values of algebraic functions, Proc. Japan. Academy, Ser. A 59 (1983), 281–284.
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Chudnovsky, D.V., Chudnovsky, G.V. (1985). Applications of Padé approximations to diophantine inequalities in values of G-functions. In: Chudnovsky, D.V., Chudnovsky, G.V., Cohn, H., Nathanson, M.B. (eds) Number Theory. Lecture Notes in Mathematics, vol 1135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074600
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