Meromorphic Functions over Non-Archimedean Fields

Language: English

Published by Springer Netherlands, 2000

0792365321 / 9780792365327

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Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH

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Druck auf Anfrage Neuware - Printed after ordering - 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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Title
Meromorphic Functions over Non-Archimedean Fields
Author
Chung-Chun Yang
Publisher
Springer Netherlands
Publication year
2000
Condition
Neu
Binding
Buch
Language
English
ISBN 10
0792365321
ISBN 13
9780792365327
Item weight
577 grams
Dimensions
241x160x22 mm

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