Meromorphic Functions over Non-Archimedean Fields - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Meromorphic Functions over Non-Archimedean Fields write by Pei-Chu Hu. This book was released on 2012-12-06. Meromorphic Functions over Non-Archimedean Fields available in PDF, EPUB and Kindle. 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).
Meromorphic Functions Over Non-Archimedean Fields
Meromorphic Functions Over Non-Archimedean Fields - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Meromorphic Functions Over Non-Archimedean Fields write by . This book was released on 2000-09-30. Meromorphic Functions Over Non-Archimedean Fields available in PDF, EPUB and Kindle.
Advances in $p$-adic and Non-Archimedean Analysis
Advances in $p$-adic and Non-Archimedean Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Advances in $p$-adic and Non-Archimedean Analysis write by M. Berz. This book was released on 2010-02-17. Advances in $p$-adic and Non-Archimedean Analysis available in PDF, EPUB and Kindle. This volume contains the proceedings of the Tenth International Conference on $p$-adic and Non-Archimedean Analysis, held at Michigan State University in East Lansing, Michigan, on June 30-July 3, 2008. This volume contains a kaleidoscope of papers based on several of the more important talks presented at the meeting. It provides a cutting-edge connection to some of the most important recent developments in the field. Through a combination of survey papers, research articles, and extensive references to earlier work, this volume allows the reader to quickly gain an overview of current activity in the field and become acquainted with many of the recent sub-branches of its development.
Spectral Theory and Analytic Geometry over Non-Archimedean Fields
Spectral Theory and Analytic Geometry over Non-Archimedean Fields - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Spectral Theory and Analytic Geometry over Non-Archimedean Fields write by Vladimir G. Berkovich. This book was released on 2012-08-02. Spectral Theory and Analytic Geometry over Non-Archimedean Fields available in PDF, EPUB and Kindle. The purpose of this book is to introduce a new notion of analytic space over a non-Archimedean field. Despite the total disconnectedness of the ground field, these analytic spaces have the usual topological properties of a complex analytic space, such as local compactness and local arcwise connectedness. This makes it possible to apply the usual notions of homotopy and singular homology. The book includes a homotopic characterization of the analytic spaces associated with certain classes of algebraic varieties and an interpretation of Bruhat-Tits buildings in terms of these analytic spaces. The author also studies the connection with the earlier notion of a rigid analytic space. Geometrical considerations are used to obtain some applications, and the analytic spaces are used to construct the foundations of a non-Archimedean spectral theory of bounded linear operators. This book requires a background at the level of basic graduate courses in algebra and topology, as well as some familiarity with algebraic geometry. It would be of interest to research mathematicians and graduate students working in algebraic geometry, number theory, and -adic analysis.
Advances in Ultrametric Analysis
Advances in Ultrametric Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Advances in Ultrametric Analysis write by Khodr Shamseddine. This book was released on 2013. Advances in Ultrametric Analysis available in PDF, EPUB and Kindle. This volume contains papers based on lectures given at the 12th International Conference on p-adic Functional Analysis, which was held at the University of Manitoba on July 2-6, 2012. Through a combination of new research articles and survey papers, this book provides the reader with an overview of current developments and techniques in non-archimedean analysis as well as a broad knowledge of some of the sub-areas of this exciting and fast-developing research area.
