Meromorphic Functions over Non-Archimedean Fields - Couverture souple

Pei-Chu Hu, Pei-Chu; Chung-Chun Yang

Couverture souple

ISBN 10 : 9048155460 ISBN 13 : 9789048155460

Editeur : Springer, 2010

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).

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2010
• Langue: anglais
• ISBN 10: 9048155460
• ISBN 13: 9789048155460
• Reliure: Broché
• Nombre de pages: 304
• Coordonnées du fabricant: non disponible