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Fundam. Prikl. Mat., 1997, Volume 3, Issue 4, Pages 1253–1260 (Mi fpm262)  

Mathematical Enlightenment

On the prooves of Lindemann's theorem and Gelfond–Schneider's theorem

A. I. Galochkin

M. V. Lomonosov Moscow State University

Abstract: The paper presents the new prooves of the Lindemann's theorem on the transcedence of the number $e^{\alpha}$ for non-zero algebraic $\alpha$ and the Gelfond–Schneider's theorem on the transcendence of the number $a^{\beta}$ for algebraic $a\ne0;1$ and algebraic irrational $\beta$. There is a difference from other prooves of Gelfond–Schneider's theorem. On the first step we construct the auxilary function with great order of zeroes at only the point $z=0$.

Full text: PDF file (279 kB)

Bibliographic databases:
UDC: 511.36
Received: 01.01.1997

Citation: A. I. Galochkin, “On the prooves of Lindemann's theorem and Gelfond–Schneider's theorem”, Fundam. Prikl. Mat., 3:4 (1997), 1253–1260

Citation in format AMSBIB
\Bibitem{Gal97}
\by A.~I.~Galochkin
\paper On the prooves of Lindemann's theorem and Gelfond--Schneider's theorem
\jour Fundam. Prikl. Mat.
\yr 1997
\vol 3
\issue 4
\pages 1253--1260
\mathnet{http://mi.mathnet.ru/fpm262}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1794513}
\zmath{https://zbmath.org/?q=an:0939.11027}


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