Geodesic
On the prooves of Lindemann's theorem and Gelfond–Schneider's theorem
Fundamentalʹnaâ i prikladnaâ matematika, Tome 3 (1997) no. 4, pp. 1253-1260 
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/
@article{FPM_1997_3_4_a21,
     author = {A. I. Galochkin},
     title = {On the prooves of {Lindemann's} theorem and {Gelfond{\textendash}Schneider's} theorem},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {1253--1260},
     year = {1997},
     volume = {3},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1997_3_4_a21/}
}
TY  - JOUR
AU  - A. I. Galochkin
TI  - On the prooves of Lindemann's theorem and Gelfond–Schneider's theorem
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 1997
SP  - 1253
EP  - 1260
VL  - 3
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/FPM_1997_3_4_a21/
LA  - ru
ID  - FPM_1997_3_4_a21
ER  - 
%0 Journal Article
%A A. I. Galochkin
%T On the prooves of Lindemann's theorem and Gelfond–Schneider's theorem
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 1997
%P 1253-1260
%V 3
%N 4
%U http://geodesic.mathdoc.fr/item/FPM_1997_3_4_a21/
%G ru
%F FPM_1997_3_4_a21

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $z=0$.