Meromorphic Functions over Non-Archimedean Fields:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
2000
|
| Schriftenreihe: | Mathematics and Its Applications
522 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Nevanlinna theory (or value distribution theory) in complex analysis is so beautiful that one would naturally be interested in determining how such a theory would look in the non Archimedean analysis and Diophantine approximations. There are two "main theorems" and defect relations that occupy a central place in N evanlinna theory. They generate a lot of applications in studying uniqueness of meromorphic functions, global solutions of differential equations, dynamics, and so on. In this book, we will introduce non-Archimedean analogues of Nevanlinna theory and its applications. In value distribution theory, the main problem is that given a holomorphic curve f : C -+ M into a projective variety M of dimension n and a family 01 of hypersurfaces on M, under a proper condition of non-degeneracy on f, find the defect relation. If 01 n is a family of hyperplanes on M = r in general position and if the smallest dimension of linear subspaces containing the image f(C) is k, Cartan conjectured that the bound of defect relation is 2n - k + 1. Generally, if 01 is a family of admissible or normal crossings hypersurfaces, there are respectively Shiffman's conjecture and Griffiths-Lang's conjecture. Here we list the process of this problem: A. Complex analysis: (i) Constant targets: R. Nevanlinna[98] for n = k = 1; H. Cartan [20] for n = k > 1; E. I. Nochka [99], [100],[101] for n > k ~ 1; Shiffman's conjecture partially solved by Hu-Yang [71J; Griffiths-Lang's conjecture (open) |
| Beschreibung: | 1 Online-Ressource (VIII, 295 p) |
| ISBN: | 9789401594158 9789048155460 |
| DOI: | 10.1007/978-94-015-9415-8 |
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| 500 | |a Nevanlinna theory (or value distribution theory) in complex analysis is so beautiful that one would naturally be interested in determining how such a theory would look in the non Archimedean analysis and Diophantine approximations. There are two "main theorems" and defect relations that occupy a central place in N evanlinna theory. They generate a lot of applications in studying uniqueness of meromorphic functions, global solutions of differential equations, dynamics, and so on. In this book, we will introduce non-Archimedean analogues of Nevanlinna theory and its applications. In value distribution theory, the main problem is that given a holomorphic curve f : C -+ M into a projective variety M of dimension n and a family 01 of hypersurfaces on M, under a proper condition of non-degeneracy on f, find the defect relation. If 01 n is a family of hyperplanes on M = r in general position and if the smallest dimension of linear subspaces containing the image f(C) is k, Cartan conjectured that the bound of defect relation is 2n - k + 1. Generally, if 01 is a family of admissible or normal crossings hypersurfaces, there are respectively Shiffman's conjecture and Griffiths-Lang's conjecture. Here we list the process of this problem: A. Complex analysis: (i) Constant targets: R. Nevanlinna[98] for n = k = 1; H. Cartan [20] for n = k > 1; E. I. Nochka [99], [100],[101] for n > k ~ 1; Shiffman's conjecture partially solved by Hu-Yang [71J; Griffiths-Lang's conjecture (open) | ||
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-015-9415-8 |
| format | Electronic eBook |
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| id | DE-604.BV042424138 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401594158 9789048155460 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859555 |
| oclc_num | 864073218 |
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| physical | 1 Online-Ressource (VIII, 295 p) |
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| publishDate | 2000 |
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| publisher | Springer Netherlands |
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| series2 | Mathematics and Its Applications |
| spelling | Hu, Pei-Chu Verfasser aut Meromorphic Functions over Non-Archimedean Fields by Pei-Chu Hu, Chung-Chun Yang Dordrecht Springer Netherlands 2000 1 Online-Ressource (VIII, 295 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 522 Nevanlinna theory (or value distribution theory) in complex analysis is so beautiful that one would naturally be interested in determining how such a theory would look in the non Archimedean analysis and Diophantine approximations. There are two "main theorems" and defect relations that occupy a central place in N evanlinna theory. They generate a lot of applications in studying uniqueness of meromorphic functions, global solutions of differential equations, dynamics, and so on. In this book, we will introduce non-Archimedean analogues of Nevanlinna theory and its applications. In value distribution theory, the main problem is that given a holomorphic curve f : C -+ M into a projective variety M of dimension n and a family 01 of hypersurfaces on M, under a proper condition of non-degeneracy on f, find the defect relation. If 01 n is a family of hyperplanes on M = r in general position and if the smallest dimension of linear subspaces containing the image f(C) is k, Cartan conjectured that the bound of defect relation is 2n - k + 1. Generally, if 01 is a family of admissible or normal crossings hypersurfaces, there are respectively Shiffman's conjecture and Griffiths-Lang's conjecture. Here we list the process of this problem: A. Complex analysis: (i) Constant targets: R. Nevanlinna[98] for n = k = 1; H. Cartan [20] for n = k > 1; E. I. Nochka [99], [100],[101] for n > k ~ 1; Shiffman's conjecture partially solved by Hu-Yang [71J; Griffiths-Lang's conjecture (open) Mathematics Global analysis (Mathematics) Functions of complex variables Differential equations, partial Analysis Functions of a Complex Variable Several Complex Variables and Analytic Spaces Mathematik Yang, Chung-Chun Sonstige oth https://doi.org/10.1007/978-94-015-9415-8 Verlag Volltext |
| spellingShingle | Hu, Pei-Chu Meromorphic Functions over Non-Archimedean Fields Mathematics Global analysis (Mathematics) Functions of complex variables Differential equations, partial Analysis Functions of a Complex Variable Several Complex Variables and Analytic Spaces Mathematik |
| title | Meromorphic Functions over Non-Archimedean Fields |
| title_auth | Meromorphic Functions over Non-Archimedean Fields |
| title_exact_search | Meromorphic Functions over Non-Archimedean Fields |
| title_full | Meromorphic Functions over Non-Archimedean Fields by Pei-Chu Hu, Chung-Chun Yang |
| title_fullStr | Meromorphic Functions over Non-Archimedean Fields by Pei-Chu Hu, Chung-Chun Yang |
| title_full_unstemmed | Meromorphic Functions over Non-Archimedean Fields by Pei-Chu Hu, Chung-Chun Yang |
| title_short | Meromorphic Functions over Non-Archimedean Fields |
| title_sort | meromorphic functions over non archimedean fields |
| topic | Mathematics Global analysis (Mathematics) Functions of complex variables Differential equations, partial Analysis Functions of a Complex Variable Several Complex Variables and Analytic Spaces Mathematik |
| topic_facet | Mathematics Global analysis (Mathematics) Functions of complex variables Differential equations, partial Analysis Functions of a Complex Variable Several Complex Variables and Analytic Spaces Mathematik |
| url | https://doi.org/10.1007/978-94-015-9415-8 |
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