Transcendental number theory

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Transcendental number theory / Alan Baker

資料種別:: 図書
出版情報:: Cambridge ; London ; New York : Cambridge University Press, 1975
形態:: x, 147 p. ; 24 cm
著者名:: Baker, Alan, 1939- <DA01519710>
ISBN:: 9780521204613 [0521204615]
書誌ID:: BA00908324

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注記:

Bibliography: p. 129
"Original papers": p. 130-144
Includes index

主題:

Numbers, Transcendental; Numbers, Transcendental--Bibliography

言語:

英語

目次情報:

Preface

The origins / 1：

Liouville's theorem

Transcendence of e / 2：

Lindemann's theorem / 3：

Linear forms in logarithms

Introduction

Corollaries

Notation

The auxiliary function / 4：

Proof of main theorem / 5：

Lower bounds for linear forms

Preliminaries

Diophantine equations

The Thue equation

The hyperelliptic equation

Curves of genus 1

Quantitative bounds

Class numbers of imaginary quadratic fields

L-functions

Limit formula

Class number 1

Class number 2

Elliptic functions / 6：

Linear equations

Periods and quasi-periods

Rational approximations to algebraic numbers / 7：

Wronskians

The index

A combinatorial lemma

Grids

The auxiliary polynomial

Successive minima

Comparison of minima / 8：

Exterior algebra / 9：

Mahler's classification / 10：

A-numbers

Algebraic dependence

Heights of polynomials

S-numbers

U-numbers

T-numbers

Metrical theory

Zeros of polynomials

Null sets

Intersections of intervals

The exponential function

Fundamental polynomials

The Siegel-Shidlovsky theorems / 11：

Basic construction

Further lemmas

Algebraic independence / 12：

Exponential polynomials

Heights

Algebraic criterion

Main arguments

Bibliography

Original papers

Further publications

New developments

Index

Preface

The origins / 1：

Liouville's theorem

Transcendence of e / 2：

Lindemann's theorem / 3：

Linear forms in logarithms

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