Diophantine Approximation on Linear Algebraic Groups
Transcendence Properties of the Exponential Function in Several Variables
634 pages, parution le 01/07/2000
Résumé
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. It includes proofs of the
main basic results (theorems of Hermite-Lindemann,
Gelfond-Schneider, 6 exponentials theorem), an introduction
to height functions and Lehmer's problem, several proofs of
Baker's theorem as well as explicit measures of linear
independence of logarithms. An original feature is the
systematic use, in proofs, of Laurent's interpolation
determinants. The most general result is the so-called
Theorem of the Linear Subgroup, an effective version of
which is also included. It yields new results of
simultaneous approximation and of algebraic independence.
Two chapters written by D. Roy provide complete and at the
same time simplified proofs of zero estimates (due to
Philippon) on linear algebraic groups.
Index
Contents
Prerequisites
Notation
- Transcendence
- Linear Independence of Logarithms and Measures
- Multiplicities in Higher Dimension
- The Linear Subgroup Theorem
- Simultaneous Approximation of Values of the Exponential Function in Several Variables
Index
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | Springer |
| Auteur(s) | Michel Waldschmidt |
| Parution | 01/07/2000 |
| Nb. de pages | 634 |
| Format | 16 x 24 |
| Couverture | Relié |
| Poids | 954g |
| Intérieur | Noir et Blanc |
| EAN13 | 9783540667858 |
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