Diophantine Approximation on Linear Algebraic Groups: Transcendence Properties of the Exponential Function in Several Variables
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2000
|
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
326 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function e z. A central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. This book includes proofs of the main basic results (theorems of Hermite-Lindemann, Gelfond-Schneider, 6 exponentials theorem), an introduction to height functions with a discussion of Lehmer's problem, several proofs of Baker's theorem as well as explicit measures of linear independence of logarithms. An original feature is that proofs make systematic use 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. 2 chapters written by D. Roy provide complete and at the same time simplified proofs of zero estimates (due to P. Philippon) on linear algebraic groups |
| Beschreibung: | 1 Online-Ressource (XXIII, 633 p) |
| ISBN: | 9783662115695 9783642086083 |
| ISSN: | 0072-7830 |
| DOI: | 10.1007/978-3-662-11569-5 |
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Datensatz im Suchindex
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-11569-5 |
| format | Electronic eBook |
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| id | DE-604.BV042423456 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662115695 9783642086083 |
| issn | 0072-7830 |
| language | English |
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| series2 | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |
| spelling | Waldschmidt, Michel Verfasser aut Diophantine Approximation on Linear Algebraic Groups Transcendence Properties of the Exponential Function in Several Variables by Michel Waldschmidt Berlin, Heidelberg Springer Berlin Heidelberg 2000 1 Online-Ressource (XXIII, 633 p) txt rdacontent c rdamedia cr rdacarrier Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 326 0072-7830 The theory of transcendental numbers is closely related to the study of diophantine approximation. This book deals with values of the usual exponential function e z. A central open problem is the conjecture on algebraic independence of logarithms of algebraic numbers. This book includes proofs of the main basic results (theorems of Hermite-Lindemann, Gelfond-Schneider, 6 exponentials theorem), an introduction to height functions with a discussion of Lehmer's problem, several proofs of Baker's theorem as well as explicit measures of linear independence of logarithms. An original feature is that proofs make systematic use 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. 2 chapters written by D. Roy provide complete and at the same time simplified proofs of zero estimates (due to P. Philippon) on linear algebraic groups Mathematics Geometry, algebraic Group theory Number theory Number Theory Algebraic Geometry Group Theory and Generalizations Mathematik Diophantische Approximation (DE-588)4135760-7 gnd rswk-swf Lineare algebraische Gruppe (DE-588)4295326-1 gnd rswk-swf Lineare algebraische Gruppe (DE-588)4295326-1 s Diophantische Approximation (DE-588)4135760-7 s 1\p DE-604 https://doi.org/10.1007/978-3-662-11569-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Waldschmidt, Michel Diophantine Approximation on Linear Algebraic Groups Transcendence Properties of the Exponential Function in Several Variables Mathematics Geometry, algebraic Group theory Number theory Number Theory Algebraic Geometry Group Theory and Generalizations Mathematik Diophantische Approximation (DE-588)4135760-7 gnd Lineare algebraische Gruppe (DE-588)4295326-1 gnd |
| subject_GND | (DE-588)4135760-7 (DE-588)4295326-1 |
| title | Diophantine Approximation on Linear Algebraic Groups Transcendence Properties of the Exponential Function in Several Variables |
| title_auth | Diophantine Approximation on Linear Algebraic Groups Transcendence Properties of the Exponential Function in Several Variables |
| title_exact_search | Diophantine Approximation on Linear Algebraic Groups Transcendence Properties of the Exponential Function in Several Variables |
| title_full | Diophantine Approximation on Linear Algebraic Groups Transcendence Properties of the Exponential Function in Several Variables by Michel Waldschmidt |
| title_fullStr | Diophantine Approximation on Linear Algebraic Groups Transcendence Properties of the Exponential Function in Several Variables by Michel Waldschmidt |
| title_full_unstemmed | Diophantine Approximation on Linear Algebraic Groups Transcendence Properties of the Exponential Function in Several Variables by Michel Waldschmidt |
| title_short | Diophantine Approximation on Linear Algebraic Groups |
| title_sort | diophantine approximation on linear algebraic groups transcendence properties of the exponential function in several variables |
| title_sub | Transcendence Properties of the Exponential Function in Several Variables |
| topic | Mathematics Geometry, algebraic Group theory Number theory Number Theory Algebraic Geometry Group Theory and Generalizations Mathematik Diophantische Approximation (DE-588)4135760-7 gnd Lineare algebraische Gruppe (DE-588)4295326-1 gnd |
| topic_facet | Mathematics Geometry, algebraic Group theory Number theory Number Theory Algebraic Geometry Group Theory and Generalizations Mathematik Diophantische Approximation Lineare algebraische Gruppe |
| url | https://doi.org/10.1007/978-3-662-11569-5 |
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