Transcendental and Algebraic Numbers

Primarily an advanced study of the modern theory of transcendental numbers, this text focuses on the theory's fundamental methods, chronicles the historical development of its methods, and explores its connections with other problems in number theory. Topics include the Thue-Siegel theorem; the Hermite-Lindemann theorem on the transcendency of the exponential function; the work of C. Siegel on the transcendency of the Bessel functions and on the solutions of other differential equations; and the Gelfond-Schneider theorem on the transcendency of alpha to the power beta. Each proof is prefaced by a brief discussion of its scheme. Reprint of 1960 English translation of the first Russian edition. Bibliography. Index.