Meromorphic Functions over Non-Archimedean Fields: 522 - Brossura

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

Brossura

ISBN 10: 9048155460 ISBN 13: 9789048155460

Casa editrice: Springer, 2010

Riassunto

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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Contenuti

Preface. 1. Basic facts in rho-adic analysis. 2. Nevanlinna theory. 3. Uniqueness of meromorphic functions. 4. Differential equations. 5. Dynamics. 6. Holomorphic curves. 7. Diophantine Approximations. A. The Cartan conjecture for moving targets. Symbols. Index.

Dettagli dell?edizione

• Editore: Springer
• Data di pubblicazione: 2010
• ISBN 10: 9048155460
• ISBN 13: 9789048155460
• Rilegatura: Copertina flessibile
• Lingua: Inglese
• Numero di pagine: 304