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

This article is cited in 1 scientific paper (total in 1 paper)

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.

Full text: PDF file (976 kB)

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

Bibliographic databases:

UDC: 511
Received: 12.03.1971

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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    Citing articles on Google Scholar: Russian citations, English citations
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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  mathnet  crossref  mathscinet  zmath  isi
  • Математические заметки Mathematical Notes
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