FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
1997, VOLUME 3, NUMBER 4, PAGES 1253-1260
A. I. Galochkin
Abstract
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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 $a\ne 0;1$
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 $z = 0$ .
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