Grundlehren der mathematischen Wissenschaften

Diophantine Approximation on Linear Algebraic Groups

Transcendence Properties of the Exponential Function in Several Variables

Authors: Waldschmidt, Michel

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eBook 101,14 €
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  • ISBN 978-3-662-11569-5
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Softcover 124,75 €
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  • ISBN 978-3-642-08608-3
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About this book

The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function e^z. A central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. This book includes proofs of the main basic results (theorems of Hermite-Lindemann, Gelfond-Schneider, 6 exponentials theorem), an introduction to height functions with a discussion of Lehmer's problem, several proofs of Baker's theorem as well as explicit measures of linear independence of logarithms. An original feature is that proofs make systematic use of Laurent's interpolation determinants. The most general result is the so-called Theorem of the Linear Subgroup, an effective version of which is also included. It yields new results of simultaneous approximation and of algebraic independence. 2 chapters written by D. Roy provide complete and at the same time simplified proofs of zero estimates (due to P. Philippon) on linear algebraic groups.

Reviews

"The present book is very nice to read, and gives a comprehensive overview of one wide aspect of Diophantine approximation. It includes the main achievements of the last several years, and points out the most interesting open questions. Moreover, each chapter is followed by numerous exercises, which provide an interesting complement of the main text. Many of them are adapted from original papers. Solutions are not given; however, there are helpful hints. This book is of great interest not only for experts in the field; it should also be recommended to anyone willing to have a taste of transcendental number theory. Undoubtedly, it will be very useful for anyone preparing a post-graduate course on Diophantine approximation."--MATHEMATICAL REVIEWS


Table of contents (15 chapters)

  • Introduction and Historical Survey

    Waldschmidt, Michel

    Pages 1-27

    Preview Buy Chapter 30,19 €
  • Transcendence Proofs in One Variable

    Waldschmidt, Michel

    Pages 29-63

    Preview Buy Chapter 30,19 €
  • Heights of Algebraic Numbers

    Waldschmidt, Michel

    Pages 65-114

    Preview Buy Chapter 30,19 €
  • The Criterion of Schneider-Lang

    Waldschmidt, Michel

    Pages 115-145

    Preview Buy Chapter 30,19 €
  • Zero Estimate, by Damien Roy

    Waldschmidt, Michel

    Pages 147-167

    Preview Buy Chapter 30,19 €

Buy this book

eBook 101,14 €
price for Spain (gross)
  • ISBN 978-3-662-11569-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 124,75 €
price for Spain (gross)
  • ISBN 978-3-540-66785-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 124,75 €
price for Spain (gross)
  • ISBN 978-3-642-08608-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Diophantine Approximation on Linear Algebraic Groups
Book Subtitle
Transcendence Properties of the Exponential Function in Several Variables
Authors
Series Title
Grundlehren der mathematischen Wissenschaften
Series Volume
326
Copyright
2000
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-11569-5
DOI
10.1007/978-3-662-11569-5
Hardcover ISBN
978-3-540-66785-8
Softcover ISBN
978-3-642-08608-3
Series ISSN
0072-7830
Edition Number
1
Number of Pages
XXIII, 633
Topics