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Nesterenko, Yu. V.

On the algebraic independence of the values of \(E\)-functions satisfying nonhomogeneous linear differential equations. (English. Russian original) Zbl 0212.39401

Math. Notes 5, 352-358 (1969); translation from Mat. Zametki 5, 587-598 (1969).
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Cited in 3 Reviews
Cited in 4 Documents

MSC:

11J85 Algebraic independence; Gel’fond’s method

Keywords:

algebraic independence; values of \(E\)-functions; nonhomogeneous linear differential equations
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Full Text: DOI

References:

[1] C. Siegel, ?Uber einige Anwendungen Diophantischer Approximationen,? Abh. Preuss Acad. Wiss., No. 1, 1-70 (1929-1930). · JFM 56.0180.05
[2] A. B. Shidlovskii, ?On a criterion for the algebraic independence of the values of a class of entire functions,? Dokl. Akad. Nauk, SSSR,100, No. 2, 221-224 (1955). · Zbl 0064.04605
[3] A. B. Shidlovskii, ?On a criterion for the algebraic independence of the values of a class of entire functions,? Izv. Akad. Nauk SSSR, Ser. Matem,23, No. 1, 35-66 (1959).
[4] A. B. Shidlovskii, ?On the transcendence and the algebraic independence of the values of E-functions satisfying second order, linear, nonhomogeneous differential equations,? Dokl. Acad. Nauk SSSR,169, No. 1, 42-45 (1966).
[5] A. B. Shidlovskii, The Transcendence of the Values of E-functions, Proc., Fourth All-Union Mathematical Congress, Leningrad, 1961 [in Russian], Vol. II, Izdat. ?Nauka,? Leningrad (1964), 147-158.
[6] B. L. van der Waerden, Moderne Algebra, Vol. II, Springer, Berlin (1937). [Russian translation], Moscow (1948). · Zbl 0016.33902
[7] I.I. Belogrivov, Candidate’s Dissertation, Moscow (1967).
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