MEROMORPHIC FUNCTIONS OVER NON-ARCHIMEDEAN FIELDS by Pei-Chu Hu, Chung-Chun Yang ( 9780792365327 )

Item Details

Title:

MEROMORPHIC FUNCTIONS OVER NON-ARCHIMEDEAN FIELDS

By:

Format:

Hardback

List price:	£89.99
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ISBN 10:

0792365321

ISBN 13:

9780792365327

Publisher:

SPRINGER

Pub. date:

30 September, 2000

Edition:

2000 ed.

Series:

Mathematics and Its Applications 522

Pages:

295

Description:

Introduces value distribution theory over non-Archimedean fields, starting with a survey of two Nevanlinna-type main theorems and defect relations for meromorphic functions and holomorphic curves. This book is useful to graduate students working in complex or diophantine approximation as well as to researchers involved in the fields of analysis.

Synopsis:

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).

Illustrations:

1 Illustrations, black and white; VIII, 295 p. 1 illus.

Publication:

Netherlands

Imprint:

Springer

Returns:

Returnable

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