剑桥数学图书馆系列：超越数理论 Transcendental Number Theory

基本信息

Series:Cambridge Mathematical Library

Format:Paperback / softback 190 pages, Worked examples or Exercises

Publisher:Cambridge University Press

Imprint:Cambridge University Press

Edition:Revised ed

ISBN:9781009229944

Published:9 Jun 2022

Weight:286g

Dimensions:152 x 227 x 17 (mm)

页面参数仅供参考，具体以实物为准

书籍简介

这本经典之作出版于1975年，系统地阐述了超限数理论，即那些不能以有理系数的代数方程的根来表达的数的理论。对它们的研究已经发展成为一个肥沃而广泛的理论，至今仍有快速的进展。本书阐述了与代数数字对数的线性形式有关的理论、施密特对Thue-Siegel-Roth定理的概括、Shidlovsky对Siegel的E函数的研究以及Sprindzuk对马勒猜想的解答。这个版本包括由David Masser撰写的介绍，描述了贝克的成就，概述了每一章的内容，并大体上解释了贝克方法的主要论点。一个新的后记列出了与贝克的工作有关的新发展。

First published in 1975, this classic book gives a systematic account of transcendental number theory, that is, the theory of those numbers that cannot be expressed as the roots of algebraic equations having rational coefficients. Their study has developed into a fertile and extensive theory, which continues to see rapid progress today. Expositions are presented of theories relating to linear forms in the logarithms of algebraic numbers, of Schmidt's generalization of the Thue-Siegel-Roth theorem, of Shidlovsky's work on Siegel's E-functions and of Sprindzuk's solution to the Mahler conjecture. This edition includes an introduction written by David Masser describing Baker's achievement, surveying the content of each chapter and explaining the main argument of Baker's method in broad strokes. A new afterword lists recent developments related to Baker's work.

作者简介

阿兰贝克是上个世纪英国知名的数学家之一。他在数论方面取得了巨大的进步，除其他成就外，他获得了Gelfond-Schneider定理的巨大概括，并利用它给出了一大类Diophantine问题的有效解决方案。这项工作开启了超限数论的新时代，并为贝克赢得了1970年的菲尔兹奖。大卫-马塞尔是巴塞尔大学数学和计算机科学系的荣誉教授。他是超越方法和应用方面的主要研究者，并作为贝克的学生帮助纠正了《超越数论》原版的证明。

Alan Baker was one of the leading British mathematicians of the past century. He took great strides in number theory by, among other achievements, obtaining a vast generalization of the Gelfond-Schneider Theorem and using it to give effective solutions to a large class of Diophantine problems. This work kicked off a new era in transcendental number theory and won Baker the Fields Medal in 1970. David Masser is Professor Emeritus in the Department of Mathematics and Computer Science at the University of Basel. He is a leading researcher in transcendence methods and applications and helped correct the proofs of the original edition of Transcendental Number Theory as Baker's student.

目录

Introduction David Masser; Preface; 1. The origins; 2. Linear forms in logarithms; 3. Lower bounds for linear forms; 4. Diophantine equations; 5. Class numbers of imaginary quadratic fields; 6. Elliptic functions; 7. Rational approximations to algebraic numbers; 8. Mahler's classification; 9. Metrical theory; 10. The exponential function; 11. The Shiegel-Shidlovsky theorems; 12. Algebraic independence; Bibliography; Original papers; Further publications; New developments; Some Developments since 1990 David Masser; Index.