The Ball and Some Hilbert Problems:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
1995
|
| Schriftenreihe: | Lectures in Mathematics ETH Zürich
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | As an interesting object of arithmetic, algebraic and analytic geometry the complex ball was born in a paper of the French Mathematician E. PICARD in 1883. In recent developments the ball finds great interest again in the framework of SHIMURA varieties but also in the theory of diophantine equations (asymptotic FERMAT Problem, see ch. VI). At first glance the original ideas and the advanced theories seem to be rather disconnected. With these lectures I try to build a bridge from the analytic origins to the actual research on effective problems of arithmetic algebraic geometry. The best motivation is HILBERT'S far-reaching program consisting of 23 problems (Paris 1900) " . . . one should succeed in finding and discussing those functions which play the part for any algebraic number field corresponding to that of the exponential function in the field of rational numbers and of the elliptic modular functions in the imaginary quadratic number field". This message can be found in the 12-th problem "Extension of KRONECKER'S Theorem on Abelian Fields to Any Algebraic Realm of Rationality" standing in the middle of HILBERTS'S program. It is dedicated to the construction of number fields by means of special value of transcendental functions of several variables. The close connection with three other HILBERT problems will be explained together with corresponding advanced theories, which are necessary to find special effective solutions, namely: 7. Irrationality and Transcendence of Certain Numbers; 21 |
| Beschreibung: | 1 Online-Ressource (160p) |
| ISBN: | 9783034890519 9783764328351 |
| DOI: | 10.1007/978-3-0348-9051-9 |
Internformat
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| 500 | |a As an interesting object of arithmetic, algebraic and analytic geometry the complex ball was born in a paper of the French Mathematician E. PICARD in 1883. In recent developments the ball finds great interest again in the framework of SHIMURA varieties but also in the theory of diophantine equations (asymptotic FERMAT Problem, see ch. VI). At first glance the original ideas and the advanced theories seem to be rather disconnected. With these lectures I try to build a bridge from the analytic origins to the actual research on effective problems of arithmetic algebraic geometry. The best motivation is HILBERT'S far-reaching program consisting of 23 problems (Paris 1900) " . . . one should succeed in finding and discussing those functions which play the part for any algebraic number field corresponding to that of the exponential function in the field of rational numbers and of the elliptic modular functions in the imaginary quadratic number field". This message can be found in the 12-th problem "Extension of KRONECKER'S Theorem on Abelian Fields to Any Algebraic Realm of Rationality" standing in the middle of HILBERTS'S program. It is dedicated to the construction of number fields by means of special value of transcendental functions of several variables. The close connection with three other HILBERT problems will be explained together with corresponding advanced theories, which are necessary to find special effective solutions, namely: 7. Irrationality and Transcendence of Certain Numbers; 21 | ||
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Datensatz im Suchindex
| _version_ | 1804153096500150272 |
|---|---|
| any_adam_object | |
| author | Holzapfel, Rolf-Peter 1942- |
| author_GND | (DE-588)117712817 |
| author_facet | Holzapfel, Rolf-Peter 1942- |
| author_role | aut |
| author_sort | Holzapfel, Rolf-Peter 1942- |
| author_variant | r p h rph |
| building | Verbundindex |
| bvnumber | BV042422285 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)905346836 (DE-599)BVBBV042422285 |
| dewey-full | 516 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516 |
| dewey-search | 516 |
| dewey-sort | 3516 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-9051-9 |
| format | Electronic eBook |
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| id | DE-604.BV042422285 |
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| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034890519 9783764328351 |
| language | English |
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| spelling | Holzapfel, Rolf-Peter 1942- Verfasser (DE-588)117712817 aut The Ball and Some Hilbert Problems by Rolf-Peter Holzapfel Basel Birkhäuser Basel 1995 1 Online-Ressource (160p) txt rdacontent c rdamedia cr rdacarrier Lectures in Mathematics ETH Zürich As an interesting object of arithmetic, algebraic and analytic geometry the complex ball was born in a paper of the French Mathematician E. PICARD in 1883. In recent developments the ball finds great interest again in the framework of SHIMURA varieties but also in the theory of diophantine equations (asymptotic FERMAT Problem, see ch. VI). At first glance the original ideas and the advanced theories seem to be rather disconnected. With these lectures I try to build a bridge from the analytic origins to the actual research on effective problems of arithmetic algebraic geometry. The best motivation is HILBERT'S far-reaching program consisting of 23 problems (Paris 1900) " . . . one should succeed in finding and discussing those functions which play the part for any algebraic number field corresponding to that of the exponential function in the field of rational numbers and of the elliptic modular functions in the imaginary quadratic number field". This message can be found in the 12-th problem "Extension of KRONECKER'S Theorem on Abelian Fields to Any Algebraic Realm of Rationality" standing in the middle of HILBERTS'S program. It is dedicated to the construction of number fields by means of special value of transcendental functions of several variables. The close connection with three other HILBERT problems will be explained together with corresponding advanced theories, which are necessary to find special effective solutions, namely: 7. Irrationality and Transcendence of Certain Numbers; 21 Mathematics Geometry, algebraic Global analysis (Mathematics) Geometry Number theory Number Theory Algebraic Geometry Analysis Mathematik Hilbertsche Probleme (DE-588)4159859-3 gnd rswk-swf Kugel (DE-588)4165914-4 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Einheitskugel (DE-588)4151312-5 gnd rswk-swf Einheitskugel (DE-588)4151312-5 s Algebraische Geometrie (DE-588)4001161-6 s Hilbertsche Probleme (DE-588)4159859-3 s 1\p DE-604 Kugel (DE-588)4165914-4 s 2\p DE-604 https://doi.org/10.1007/978-3-0348-9051-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Holzapfel, Rolf-Peter 1942- The Ball and Some Hilbert Problems Mathematics Geometry, algebraic Global analysis (Mathematics) Geometry Number theory Number Theory Algebraic Geometry Analysis Mathematik Hilbertsche Probleme (DE-588)4159859-3 gnd Kugel (DE-588)4165914-4 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Einheitskugel (DE-588)4151312-5 gnd |
| subject_GND | (DE-588)4159859-3 (DE-588)4165914-4 (DE-588)4001161-6 (DE-588)4151312-5 |
| title | The Ball and Some Hilbert Problems |
| title_auth | The Ball and Some Hilbert Problems |
| title_exact_search | The Ball and Some Hilbert Problems |
| title_full | The Ball and Some Hilbert Problems by Rolf-Peter Holzapfel |
| title_fullStr | The Ball and Some Hilbert Problems by Rolf-Peter Holzapfel |
| title_full_unstemmed | The Ball and Some Hilbert Problems by Rolf-Peter Holzapfel |
| title_short | The Ball and Some Hilbert Problems |
| title_sort | the ball and some hilbert problems |
| topic | Mathematics Geometry, algebraic Global analysis (Mathematics) Geometry Number theory Number Theory Algebraic Geometry Analysis Mathematik Hilbertsche Probleme (DE-588)4159859-3 gnd Kugel (DE-588)4165914-4 gnd Algebraische Geometrie (DE-588)4001161-6 gnd Einheitskugel (DE-588)4151312-5 gnd |
| topic_facet | Mathematics Geometry, algebraic Global analysis (Mathematics) Geometry Number theory Number Theory Algebraic Geometry Analysis Mathematik Hilbertsche Probleme Kugel Algebraische Geometrie Einheitskugel |
| url | https://doi.org/10.1007/978-3-0348-9051-9 |
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