On the algebraic structure of functional matrices of special form. (English. Russian original) Zbl 0901.41012

Zudilin, V. V.

Math. Notes 60, No. 6, 642-648 (1996); translation from Mat. Zametki 60, No. 6, 851-860 (1996).

The graded Padé approximants introduced by G. V. Chudnovsky in 1984 to study the transcendence of numbers was completed by some initially missing algebraic proofs by the author of the present paper. Here, the author follows the investigation of arising matrices in the construction of the above approximants and shows some interesting combinatorial laws related to these approximants.

Reviewer: J.Gilewicz (Marseille)

MSC:

41A21	Padé approximation
11J99	Diophantine approximation, transcendental number theory

Keywords:

graded Padé approximants

References:

[1]	G. V. Chudnovsky, ”On some applications of diophantine approximations,”Proc. Nat. Acad. Sci. USA.,81, 1926–1930 (1984). · Zbl 0544.10034
[2]	V. V. Zudilin, ”Lower estimates of polynomials in values of certain entire functions,”Mat. Sb. [Math. USSR-Sb.],187, No. 12, 57–80 (1996). · Zbl 0878.11030
[3]	V. V. Zudilin, ”Rational approximations of a certain class of entire functions,”Mat. Sb. [Math. USSR-Sb.],186, No. 4, 89–124 (1995). · Zbl 0848.11031
[4]	V. V. Zudilin, ”On the measure of the irrationality of the values ofG-functions,”Izv. Ross. Akad. Nauk. Ser. Mat. [Math. USSR-Izv.]60, No. 1, 87–114 (1996). · Zbl 0931.11025
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[6]	A. I. Galochkin, ”Estimates for the number of zeros of certain functions with algebraic coefficients of the Taylor series,”Mat. Zametki [Math. Notes] (1997) (to appear). · Zbl 0968.11028