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Mat. Zametki, 1968, Volume 3, Issue 1, Pages 51–58 (Mi mz6651)  

The algebraic independence of certain transcendental numbers

A. A. Shmelev


Abstract: Given the three numbers of, $a^\beta_1$, $a^\beta_2$, and $\frac{\ln a_2}{\ln a_1}$, where $a_1$ and $a_2$ are algebraic numbers whose logarithms are linearly independent in a rational field and $\beta$ is a quadratic irrationality, it is shown that they are not all expressible algebraically in terms of one of them.

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English version:
Mathematical Notes, 1968, 3:1, 31–35

Bibliographic databases:

UDC: 511
Received: 31.05.1967

Citation: A. A. Shmelev, “The algebraic independence of certain transcendental numbers”, Mat. Zametki, 3:1 (1968), 51–58; Math. Notes, 3:1 (1968), 31–35

Citation in format AMSBIB
\Bibitem{Shm68}
\by A.~A.~Shmelev
\paper The algebraic independence of certain transcendental numbers
\jour Mat. Zametki
\yr 1968
\vol 3
\issue 1
\pages 51--58
\mathnet{http://mi.mathnet.ru/mz6651}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=237439}
\zmath{https://zbmath.org/?q=an:0162.34802|0155.37902}
\transl
\jour Math. Notes
\yr 1968
\vol 3
\issue 1
\pages 31--35
\crossref{https://doi.org/10.1007/BF01386962}


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