E-Book, Englisch, Band 326, 633 Seiten, eBook
Waldschmidt Diophantine Approximation on Linear Algebraic Groups
2000
ISBN: 978-3-662-11569-5
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
Transcendence Properties of the Exponential Function in Several Variables
E-Book, Englisch, Band 326, 633 Seiten, eBook
Reihe: Grundlehren der mathematischen Wissenschaften
ISBN: 978-3-662-11569-5
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark
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.
Zielgruppe
Research
Autoren/Hrsg.
Weitere Infos & Material
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 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
