This manual provides comprehensive information regarding the theory of transcendental and algebraic numbers, focusing on fundamental methods and their historical development. Authored by a distinguished Soviet mathematician, this treatment delves into advanced concepts and their connections with other areas of number theory. Key topics explored include the Thue-Siegel theorem, the Hermite-Lindemann theorem, and the work of C. Siegel on the transcendency of various functions. The text also examines the Gelfond-Schneider theorem and offers detailed proofs, each prefaced by a scheme to aid understanding.
The purpose of this manual is to serve as an in-depth resource for students and researchers in number theory. It systematically covers the theoretical underpinnings and practical applications of transcendental and algebraic number theory. The structured approach, with proofs accompanied by explanatory schemes, ensures clarity and facilitates a thorough grasp of complex mathematical concepts. This work is essential for anyone seeking to understand the modern theory of numbers and its intricate relationships with other mathematical disciplines.
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.
Author: Gelfond, A. O.
Publisher: Dover Publications
Illustration: N
Language: ENG
Title: Transcendental and Algebraic Numbers
Pages: 00208 (Encrypted EPUB)
On Sale: 2015-01-05
SKU-13/ISBN: 9780486495262
Category: Mathematics : Number Theory
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.
Author: Gelfond, A. O.
Publisher: Dover Publications
Illustration: N
Language: ENG
Title: Transcendental and Algebraic Numbers
Pages: 00208 (Encrypted EPUB)
On Sale: 2015-01-05
SKU-13/ISBN: 9780486495262
Category: Mathematics : Number Theory
