超越数与代数Transcendental and algebraic numbers

2003-2  

Oversea Publishing House  

A.O.Gelfond　著  

188  

Primarily an advanced study of the modern theory of transcendental numbers, this text focuses on the theory's fundamental 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 transcendency of the Bessel functions; more.

FOREWORDCHAPTER Ⅰ. The approximation of algebraic irrationalities 1. Introduction 2. Auxiliary lemmas 3. Fundamental theorems 4. Applications of the fundamental theoremsCHAPTER Ⅱ. Transcendence of values of analytic functions whose Taylor series have algebraic coefficients 1. Introduction. The Hermite and Lindemann theorems 2. Further development of the ideas of Hermite and Lindemann 3. Auxiliary propositions and definitions 4. General theorem on the algebraic independence of values of an E-function and consequences of it 5. Problems concerning transcendence and algebraic independence, over the rational field, of numbers defined by infinite series or which are roots of algebraic or transcendental equationsCHAPTER Ⅲ. Arithmetic properties of the set of values of an analytic function whose argument assumes values in an algebraic field; transcendence problems 1. Integrity of analytic functions 2. The Euler-Hilbert problem 3. Problems concerning measure of transcendence and further development of methods 4. Formulation of fundamental theorems and auxiliary propositions 5. Proof of the fundamental theoremsLITERATUREINDEX

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