Transcendental and Algebraic Numbers (eBook)

A. O. Gelfond (Autor)

eBook Download: EPUB

2015
208 Seiten
Dover Publications (Verlag)
978-0-486-80225-1 (ISBN)

Infos

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.

Autor

Alexander Osipovich Gelfond (1906–68) was a prominent Soviet mathematician.

Inhalt

1. The approximation of algebraic irrationalities2. Transcendence of values of analytic functions whose Taylor series have algebraic coefficients3. Arithmetic properties of the set of values of an analytic function whose argument assumes values in an algebraic field; transcendence problems. Literature. Index.

Produkt-Details

• Erscheint lt. Verlag: 5.1.2015
• Reihe/Serie: Dover Books on Mathematics
• Übersetzer: Leo F. Boron
• Sprache: englisch
• Maße: 140 x 140 mm
• Gewicht: 454 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
• Schlagworte: advanced algebra • advanced mathematics • Algebra • algebraic functions • alpha • Approximating • arithmetic • Bessel functions • Beta • books on math • c. siegel • Differential Equations • gelfond schneider theorem • Gelfond-Schneider Theorem • hermite lindemann theorem • Hermite-Lindemann theorem • mathematical equations • mathematical studies • mathematical theories • Mathematics • Non-fiction • proofs • soviet mathematician • thue siegel theorem • Thue-Siegel Theorem • transcendency of alpha to the power beta • transcendency of the bessel functions • transcendency of the exponential function • Transcendental numbers
• ISBN-10: 0-486-80225-6 / 0486802256
• ISBN-13: 978-0-486-80225-1 / 9780486802251