Gelfond, A. O. Transcendental and algebraic numbers. (English. Russian original) Zbl 0090.26103 New York: Dover Publications, Inc. vii, 190 p. (1960). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 12 ReviewsCited in 80 Documents MSC: 11J81 Transcendence (general theory) 11J82 Measures of irrationality and of transcendence 11-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory 11J17 Approximation by numbers from a fixed field 11J61 Approximation in non-Archimedean valuations 11J68 Approximation to algebraic numbers 11J89 Transcendence theory of elliptic and abelian functions 11J91 Transcendence theory of other special functions Keywords:transcendental numbers; algebraic numbers; Thue-Siegel theorem; approximation of algebraic numbers by numbers from a fixed algebraic field; Hermite-Lindemann theorem; transcendence of exponential function; transcendence of the solutions of linear differential equations; Bessel functions; functional equation; Gelfond-Schneider theorem; transcendence of \(a^b\); Schneider theorem on elliptic functions; measure of irrationality of \(\log a/\log b\); algebraic p-adic numbers Citations:Zbl 0048.03303 × Cite Format Result Cite Review PDF