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Fundamentalnaya i Prikladnaya Matematika, 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
Full-text PDF (279 kB) Citations (1)
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 $z=0$.
Received: 01.01.1997
Bibliographic databases:
Document Type: Popular science or education materials
UDC: 511.36
Language: Russian
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://mathscinet.ams.org/mathscinet-getitem?mr=1794513}
\zmath{https://zbmath.org/?q=an:0939.11027}
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  • This publication is cited in the following 1 articles:
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