Diophantine Approximation on Linear Algebraic Groups
Transcendence Properties of the Exponential Function in Several Variables
(Sprache: Englisch)
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...
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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.
Inhaltsverzeichnis zu „Diophantine Approximation on Linear Algebraic Groups “
1. Introduction and Historical Survey Part I. Linear Independence of Logarithms of Algebraic Numbers
2. Transcendence Proofs in One Variable
3. Heights of Algebraic Numbers
4. The Criterion of Schneider-Lang
5. Zero Estimate
6. Linear Independence of Logarithms of Algebraic Numbers
Part II. Measures of Linear Independence
7. A First Measure with a Simple Proof
8. Zero Estimate (Continued), by Damien ROY
9. Refined Measure
Part III. Multiplicities in Higher Dimension
10. Multiplicity Estimates, by Damien ROY
11. Interpolation Determinants with One Derivative
12. On Baker's Method Part IV. The Linear Subgroup Theorem
13. Points Whose Coordinates are Logarithms of Algebraic Numbers
14. Lower Bounds for the Rank of Matrices Part V. Simultaneous Approximation of Values of the Exponential Function in Several Variables
15. A Quantitative Version of the Linear Subgroup Theorem
16. Applications to Diophantine Approximation
17. Algebraic Independence References.
Bibliographische Angaben
- Autor: Michel Waldschmidt
- 2000, 633 Seiten, Maße: 16,3 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer
- ISBN-10: 3540667857
- ISBN-13: 9783540667858
- Erscheinungsdatum: 26.05.2000
Sprache:
Englisch
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