Meromorphic Functions over Non-archimedean Fields - Mathematics and Its Applications - Pei-chu Hu - Kirjat - Springer - 9789048155460 - tiistai 7. joulukuuta 2010
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Meromorphic Functions over Non-archimedean Fields - Mathematics and Its Applications 1st Ed. Softcover of Orig. Ed. 2000 edition

Pei-chu Hu

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Meromorphic Functions over Non-archimedean Fields - Mathematics and Its Applications 1st Ed. Softcover of Orig. Ed. 2000 edition

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).


295 pages, 1 black & white illustrations, biography

Media Kirjat     Paperback Book   (Kirja pehmeillä kansilla ja liimatulla selällä)
Julkaisupäivämäärä tiistai 7. joulukuuta 2010
ISBN13 9789048155460
Tuottaja Springer
Sivujen määrä 295
Mitta 155 × 235 × 16 mm   ·   426 g
Kieli English  

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