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Mat. Zametki, 1974, Volume 15, Issue 4, Pages 661–672 (Mi mz7390)  

This article is cited in 3 scientific papers (total in 3 papers)

Algebraic independence of some values of the exponential function

G. V. Chudnovskii

National Taras Shevchenko University of Kyiv

Abstract: We prove general results concerning the algebraic independence of three values of the exponential function. For $\beta$ algebraic and of degree 7 and $\alpha$ algebraic and $\neq0, 1$ there exist among the numbers $\alpha^\beta,…,\alpha^{\beta^6}$ three which are algebraically independent. The proof employs a method due to A. O. Gel'fond and N. I. Fel'dman.

Full text: PDF file (844 kB)

English version:
Mathematical Notes, 1974, 15:4, 391–398

Bibliographic databases:

UDC: 511
Received: 22.01.1973

Citation: G. V. Chudnovskii, “Algebraic independence of some values of the exponential function”, Mat. Zametki, 15:4 (1974), 661–672; Math. Notes, 15:4 (1974), 391–398

Citation in format AMSBIB
\Bibitem{Chu74}
\by G.~V.~Chudnovskii
\paper Algebraic independence of some values of the exponential function
\jour Mat. Zametki
\yr 1974
\vol 15
\issue 4
\pages 661--672
\mathnet{http://mi.mathnet.ru/mz7390}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=357337}
\zmath{https://zbmath.org/?q=an:0295.10027}
\transl
\jour Math. Notes
\yr 1974
\vol 15
\issue 4
\pages 391--398
\crossref{https://doi.org/10.1007/BF01095134}


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

    This publication is cited in the following articles:
    1. Yu. V. Nesterenko, “On algebraic independence of algebraic powers of algebraic numbers”, Math. USSR-Sb., 51:2 (1985), 429–454  mathnet  crossref  mathscinet  zmath  isi
    2. A. A. Shmelev, “On a simultaneous approximation of logarithms and algebraic powers of algebraic numbers”, Math. Notes, 56:1 (1994), 734–744  mathnet  crossref  mathscinet  zmath  isi
    3. A. Ya. Yanchenko, “On the measure of algebraic independence of values of derivatives of a $p$-adic modular function”, Math. Notes, 61:3 (1997), 352–359  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Математические заметки Mathematical Notes
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