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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 1972, Volume 11, Issue 6, Pages 635–644 (Mi mz9831)

On the question of the algebraic independence of algebraic powers of algebraic numbers

A. A. Shmelev

M. V. Lomonosov Moscow State University

Abstract: We obtain results showing that transcendental numbers of the form $a^\beta$, where $a\ne0,1$, $\beta$ is irrational, and $a$ and $\beta$ are algebraic numbers, cannot be expressed algebraically in terms of two of the numbers. The proof is carried out by A. O. Gel'fond's method.

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English version:
Mathematical Notes, 1972, 11:6, 387–392

Bibliographic databases:

UDC: 511

Citation: A. A. Shmelev, “On the question of the algebraic independence of algebraic powers of algebraic numbers”, Mat. Zametki, 11:6 (1972), 635–644; Math. Notes, 11:6 (1972), 387–392

Citation in format AMSBIB
\Bibitem{Shm72} \by A.~A.~Shmelev \paper On the question of the algebraic independence of algebraic powers of algebraic numbers \jour Mat. Zametki \yr 1972 \vol 11 \issue 6 \pages 635--644 \mathnet{http://mi.mathnet.ru/mz9831} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=299563} \zmath{https://zbmath.org/?q=an:0254.10029} \transl \jour Math. Notes \yr 1972 \vol 11 \issue 6 \pages 387--392 \crossref{https://doi.org/10.1007/BF01093723} 

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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
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