Buch, Englisch, Band 326, 633 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 1003 g
Transcendence Properties of the Exponential Function in Several Variables
Buch, Englisch, Band 326, 633 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 1003 g
Reihe: Grundlehren der mathematischen Wissenschaften
ISBN: 978-3-642-08608-3
Verlag: Springer
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.
Fachgebiete
- Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
- Mathematik | Informatik Mathematik Algebra Zahlentheorie
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
- Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
Weitere Infos & Material
1. Introduction and Historical Survey.- 2. Transcendence Proofs in One Variable.- 3. Heights of Algebraic Numbers.- 4. The Criterion of Schneider-Lang.- 5. Zero Estimate, by Damien Roy.- 6. Linear Independence of Logarithms of Algebraic Numbers.- 7. Homogeneous Measures of Linear Independence.- 8. Multiplicity Estimates, by Damien Roy.- 9. Refined Measures.- 10. On Baker’s Method.- 11. Points Whose Coordinates are Logarithms of Algebraic Numbers.- 12. Lower Bounds for the Rank of Matrices.- 13. A Quantitative Version of the Linear Subgroup Theorem.- 14. Applications to Diophantine Approximation.- 15. Algebraic Independence.- References.
