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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:   Print 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 pages ; 24 cm.
Contents: 1. Introduction and Historical Survey --
Pt. I. Transcendence --
2. Transcendence Proofs in One Variable --
3. Heights of Algebraic Numbers --
4. The Criterion of Schneider-Lang --
Pt. II. Linear Independence of Logarithms and Measures --
5. Zero Estimate / Damien Roy --
6. Linear Independence of Logarithms of Algebraic Numbers --
7. Homogeneous Measures of Linear Independence --
Pt. III. Multiplicities in Higher Dimension --
8. Multiplicity Estimates / Damien Roy --
9. Refined Measures --
10. On Baker's Method --
Pt. IV. The Linear Subgroup Theorem --
11. Points Whose Coordinates are Logarithms of Algebraic Numbers --
12. Lower Bounds for the Rank of Matrices --
Pt. V. Simultaneous Approximation of Values of the Exponential Function in Several Variables --
13. A Quantitative Version of the Linear Subgroup Theorem --
14. Applications to Diophantine Approximation --
15. Algebraic Independence.
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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