FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1997, VOLUME 3, NUMBER 4, PAGES 1253-1260

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

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 $e$a for non-zero algebraic $$a and the Gelfond--Schneider's theorem on the transcendence of the number $a$b for algebraic $a$¹ 0; 1 and algebraic irrational $$b. 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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