Diophantine Approximation on Linear Algebraic Groups: Transcendence Properties of the Exponential Function in Several Variables

Waldschmidt, Michel

ISBN 10: 3540667857 / ISBN 13: 9783540667858

Published by U.S.A.: Springer, 2000

About this Item

**INTERNATIONAL EDITION** Read carefully before purchase: This book is the international edition in mint condition with the different ISBN and book cover design, the major content is printed in full English as same as the original North American edition. The book printed in black and white, generally send in twenty-four hours after the order confirmed. All shipments go through via USPS/UPS/DHL with tracking numbers. Great professional textbook selling experience and expedite shipping service.

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Bibliographic Details

• Title: Diophantine Approximation on Linear Algebraic Groups: Transcendence Properties of the Exponential Function in Several Variables
• Publisher: U.S.A.: Springer
• Publication Date: 2000
• Language: English
• ISBN 10: 3540667857
• ISBN 13: 9783540667858
• Binding: Soft cover
• Edition: 1st Edition, International Edition
• Condition: New
• Dust Jacket Condition: New

About this title

Synopsis

The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function ez: a central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. Two chapters provide complete and simplified proofs of zero estimates (due to Philippon) on linear algebraic groups.

From the Back Cover

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) onlinear algebraic groups.