Meromorphic Functions over Non-Archimedean Fields
Authors: Pei-Chu Hu, Chung-Chun Yang
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- About this book
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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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Bibliographic Information
- Bibliographic Information
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- Book Title
- Meromorphic Functions over Non-Archimedean Fields
- Authors
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- Pei-Chu Hu
- Chung-Chun Yang
- Series Title
- Mathematics and Its Applications
- Series Volume
- 522
- Copyright
- 2000
- Publisher
- Springer Netherlands
- Copyright Holder
- Springer Science+Business Media Dordrecht
- eBook ISBN
- 978-94-015-9415-8
- DOI
- 10.1007/978-94-015-9415-8
- Hardcover ISBN
- 978-0-7923-6532-7
- Softcover ISBN
- 978-90-481-5546-0
- Edition Number
- 1
- Number of Pages
- VIII, 295
- Number of Illustrations and Tables
- 1 b/w illustrations
- Topics
