Yu. V. Nesterenko, “On the algebraic independence of the values of $E$-functions satisfying nonhomogeneous linear differential equations”, Mat. Zametki, 5:5 (1969), 587–598; Math. Notes, 5:5 (1969), 352

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Matematicheskie Zametki, 1969, Volume 5, Issue 5, Pages 587–598 (Mi mzm6871)

This article is cited in 13 scientific papers (total in 13 papers)

On the algebraic independence of the values of $E$-functions satisfying nonhomogeneous linear differential equations

Yu. V. Nesterenko

M. V. Lomonosov Moscow State University

Full-text PDF (776 kB) Citations (13)

Abstract: We prove a theorem which reduces the investigation of the algebraic independence of solutions of linear nonhomogeneous systems of differential equations to the investigation of homogeneous systems. We use this theorem to prove the algebraic independence of the values of certain $E$-functions.

Received: 26.07.1968

English version:
Mathematical Notes, 1969, Volume 5, Issue 5, Pages 352–358
DOI: https://doi.org/10.1007/BF01112185

Bibliographic databases:

UDC: 511

Language: Russian

Citation: Yu. V. Nesterenko, “On the algebraic independence of the values of $E$-functions satisfying nonhomogeneous linear differential equations”, Mat. Zametki, 5:5 (1969), 587–598; Math. Notes, 5:5 (1969), 352–358

Citation in format AMSBIB

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\by Yu.~V.~Nesterenko

\paper On the algebraic independence of the values of $E$-functions satisfying nonhomogeneous linear differential equations

\jour Mat. Zametki

\yr 1969

\vol 5

\issue 5

\pages 587--598

\mathnet{http://mi.mathnet.ru/mzm6871}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=246824}

\zmath{https://zbmath.org/?q=an:0212.39401}

\transl

\jour Math. Notes

\yr 1969

\vol 5

\issue 5

\pages 352--358

\crossref{https://doi.org/10.1007/BF01112185}

Linking options:

https://www.mathnet.ru/eng/mzm6871

https://www.mathnet.ru/eng/mzm/v5/i5/p587

This publication is cited in the following 13 articles:

A. Kh. Munos Vaskes, “Arifmeticheskie svoistva znachenii nekotorykh gipergeometricheskikh $F$-ryadov”, Chebyshevskii sb., 22:2 (2021), 519–527
V. G. Chirskii, “Arithmetic properties of generalized hypergeometric $F$-series”, Dokl. Math., 98:3 (2018), 589–591
V. A. Gorelov, “On the Algebraic Properties of Solutions of Inhomogeneous Hypergeometric Equations”, Math. Notes, 99:5 (2016), 663–675
P. Yu. Kozlov, “On the algebraic independence of functions of a certain class”, Izv. Math., 77:1 (2013), 20–29
W. V. Zudilin, “Cancellation of factorials”, Sb. Math., 192:8 (2001), 1181–1207
V. Kh. Salikhov, “Criterion for the algebraic independence of values of hypergeometric $E$-functions (even case)”, Math. Notes, 64:2 (1998), 230–239
M. A. Cherepnev, “Algebraic independence of values of hypergeometric $E$-functions”, Math. Notes, 57:6 (1995), 630–642
M. A. Cherepnev, “On algebraic independence of some subclasses of hypergeometric functions”, Math. Notes, 55:1 (1994), 78–85
V. Kh. Salikhov, “A criterion for the algebraic independence of values of a class of hypergeometric $E$-functions”, Math. USSR-Sb., 69:1 (1991), 203–226
V. Kh. Salikhov, “On the algebraic irreducibility of the set of linear differential equations”, Math. USSR-Izv., 26:1 (1986), 185–200
V. Kh. Salikhov, “On the algebraic independence of the values of hypergeometric $E$-functions”, Russian Math. Surveys, 39:2 (1984), 191–192
V. Kh. Salikhov, “On differential irreducibility of a class of differential equations”, Math. USSR-Izv., 16:1 (1981), 165–189
Yu. V. Nesterenko, “On the algebraic dependence of the components of solutions of a system of linear differential equations”, Math. USSR-Izv., 8:3 (1974), 501–518

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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