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Diophantine approximation on linear algebraic groups : transcendence properties of the exponential function in several variables

Author: Michel Waldschmidt
Publisher: Berlin ; New York : Springer, ©2000.
Series: Grundlehren der mathematischen Wissenschaften, 326.
Edition/Format:   Book : EnglishView all editions and formats
Database:WorldCat
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Michel Waldschmidt
ISBN: 3540667857 9783540667858 364208608X 9783642086083
OCLC Number: 44019396
Description: xxiii, 633 p. ; 24 cm.
Contents: Introduction and Historical Survey.- Part I. Linear Independence of Logarithms of Algebraic Numbers. Transcendence Proofs in One Variable. Heights of Algebraic Numbers. The Criterion of Schneider-Lang. Zero Estimate. Linear Independence of Logarithms of Algebraic Numbers.- Part II. Measures of Linear Independence. A First Measure with a Simple Proof. Zero Estimate (Continued), by Damien ROY. Refined Measure.- Part III. Multiplicities in Higher Dimension Multiplicity Estimates, by Damien ROY. Interpolation Determinants with One Derivative. On Baker's Method.- Part IV. The Linear Subgroup Theorem. Points Whose Coordinates are Logarithms of Algebraic Numbers. Lower Bounds for the Rank of Matrices.- Part V. Simultaneous Approximation of Values of the Exponential Function in Several Variables. A Quantitative Version of the Linear Subgroup Theorem. Applications to Diophantine Approximation. Algebraic Independence.- References.
Series Title: Grundlehren der mathematischen Wissenschaften, 326.
Responsibility: Michel Waldschmidt.
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"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 Read more...

 
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