Meromorphic Functions Over Non-Archimedean Fields

Hu, Pei-Chu; Chung-Chun Yang

ISBN 10: 0792365321 / ISBN 13: 9780792365327

Published by Kluwer Academic Publishers, 2000

About this Item

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. Series: Mathematics and its Applications. Num Pages: 295 pages, 1 black & white illustrations, biography. BIC Classification: PBKD. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 235 x 155 x 19. Weight in Grams: 609. . 2000. Hardback. . . . .

Seller Inventory # V9780792365327

Bibliographic Details

• Title: Meromorphic Functions Over Non-Archimedean Fields
• Publisher: Kluwer Academic Publishers
• Publication Date: 2000
• Language: English
• ISBN 10: 0792365321
• ISBN 13: 9780792365327
• Binding: Hardcover
• Condition: New

About this title

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).