Meromorphic Functions over Non-Archimedean Fields (Mathematics and Its Applications, 522)

Pei-Chu Hu, Chung-Chun Yang

ISBN 10: 9048155460 / ISBN 13: 9789048155460

Edité par Springer, 2010

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N° de réf. du vendeur ERICA82990481554606

Détails bibliographiques

• Titre: Meromorphic Functions over Non-Archimedean Fields (Mathematics and Its Applications, 522)
• Éditeur: Springer
• Date de parution: 2010
• Langue: anglais
• ISBN à 10 chiffres: 9048155460
• ISBN à 13 chiffres: 9789048155460
• Reliure: Paperback
• État de l'article: New
• Type de livre: book

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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).