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Synopsis
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.
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About the Author
Alexander Osipovich Gelfond (1906–68) was a prominent Soviet mathematician.
From the Back Cover
Primarily an advanced study of the modern theory of transcendental and algebraic numbers, this treatment by a distinguished Soviet mathematician focuses on the theory's fundamental methods. The text also chronicles the historical development of the theory's methods and explores the connections with other problems in number theory. The problem of approximating algebraic numbers is also studied as a case in the theory of transcendental numbers.
Topics include the Thue-Siegel theorem, the Hermite-Lindemann theorem on the transcendency of the exponential function, and the work of C. Siegel on the transcendency of the Bessel functions and of the solutions of other differential equations. The final chapter considers the Gelfond-Schneider theorem on the transcendency of alpha to the power beta. Each proof is prefaced by a brief discussion of its scheme, which provides a helpful guide to understanding the proof's progression.
Dover (2015) republication of the Dover 1960 English translation of the first Russian edition.
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