Mathematics and Its Applications

Meromorphic Functions over Non-Archimedean Fields

Authors: Pei-Chu Hu, Chung-Chun Yang

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About this book

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).

Table of contents (7 chapters)

Table of contents (7 chapters)
  • Basic facts in p-adic analysis

    Pages 1-31

    Hu, Pei-Chu (et al.)

  • Nevanlinna theory

    Pages 33-75

    Hu, Pei-Chu (et al.)

  • Uniqueness of meromorphic functions

    Pages 77-113

    Hu, Pei-Chu (et al.)

  • Differential equations

    Pages 115-138

    Hu, Pei-Chu (et al.)

  • Dynamics

    Pages 139-175

    Hu, Pei-Chu (et al.)

Buy this book

eBook n/a
  • ISBN 978-94-015-9415-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
Hardcover n/a
  • ISBN 978-0-7923-6532-7
  • Free shipping for individuals worldwide
Softcover n/a
  • ISBN 978-90-481-5546-0
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Meromorphic Functions over Non-Archimedean Fields
Authors
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
1 b/w illustrations
Topics