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A criterion for algebraic dependence of transcendental numbers

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Abstract

We obtain a theorem concerning the algebraic dependence of the p+1 numbersθ,θ 1 ...θ p subject to the condition that the numbersθ 1 , ...,θ p are algebraically independent and possess a “sufficiently good” estimate of measure of algebraic independence.

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Authors and Affiliations

  1. Institute of Electronic Control Machines, USSR

    A. A. Shmelev

Authors
  1. A. A. Shmelev
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Translated from Matematicheskie Zametki, Vol. 16, No. 4, pp. 553–562, October, 1974.

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Shmelev, A.A. A criterion for algebraic dependence of transcendental numbers. Mathematical Notes of the Academy of Sciences of the USSR 16, 921–926 (1974). https://doi.org/10.1007/BF01104256

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  • DOI: https://doi.org/10.1007/BF01104256

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