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

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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.

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    Yu. V. Nesterenko

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  1. Yu. V. Nesterenko
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Translated from Matematicheski Zametki, Vol. 5, No. 5, pp. 587–598, May, 1969.

In conclusion I wish to thank my supervisor. A. B. Shidlovskii, for posing this problem and for help in the preparation of this note.

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Nesterenko, Y.V. On the algebraic independence of the values of E-functions satisfying nonhomogeneous linear differential equations. Mathematical Notes of the Academy of Sciences of the USSR 5, 352–358 (1969). https://doi.org/10.1007/BF01112185

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  • DOI: https://doi.org/10.1007/BF01112185

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