On the prooves of Lindemann's theorem and Gelfond--Schneider's theorem
Fundamentalʹnaâ i prikladnaâ matematika, Tome 3 (1997) no. 4, pp. 1253-1260
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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 $z=0$.
@article{FPM_1997_3_4_a21,
author = {A. I. Galochkin},
title = {On the prooves of {Lindemann's} theorem and {Gelfond--Schneider's} theorem},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {1253--1260},
publisher = {mathdoc},
volume = {3},
number = {4},
year = {1997},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_1997_3_4_a21/}
}
A. I. Galochkin. On the prooves of Lindemann's theorem and Gelfond--Schneider's theorem. Fundamentalʹnaâ i prikladnaâ matematika, Tome 3 (1997) no. 4, pp. 1253-1260. http://geodesic.mathdoc.fr/item/FPM_1997_3_4_a21/