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

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.

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

Bibliographic databases:

UDC: 511

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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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
2. A. A. Shmelev, “On a simultaneous approximation of logarithms and algebraic powers of algebraic numbers”, Math. Notes, 56:1 (1994), 734–744
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
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