×

zbMATH — the first resource for mathematics

On the algebraic structure of functional matrices of special form. (English. Russian original) Zbl 0901.41012
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.
MSC:
41A21 Padé approximation
11J99 Diophantine approximation, transcendental number theory
PDF BibTeX XML Cite
Full Text: DOI
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
[5] A. B. Shidlovskii,Transcendental Numbers [in Russian], Nauka, Moscow (1987); English transl.: Walter de Gruyter, Berlin-New York (1989).
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.