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Meromorphic Functions Over Non-Archimedean Fields by Pei-Chu Hu

Meromorphic Functions Over Non-Archimedean Fields

by Pei-Chu Hu
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Book cover type: Paperback
  • ISBN13: 9789048155460
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 295
  • Original Price: EUR 49.99
  • Language: English
  • Edition: N/A
  • Item Weight: 462 grams
  • BISAC Subject(s): Mathematical Analysis, General, and Functional Analysis

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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