Last edited by Douzshura
Friday, April 17, 2020 | History

5 edition of Meromorphic functions over non-archimedean fields found in the catalog.

# Meromorphic functions over non-archimedean fields

Written in English

Subjects:
• Nevanlinna theory.,
• Diophantine approximation.,
• Functional analysis.

• Edition Notes

Includes bibliographical references (p. 281-289) and index.

Classifications The Physical Object Statement Pei-Chu Hu and Chung-Chun Yang. Series Mathematics and its applications -- v. 522, Mathematics and its applications (Kluwer Academic Publishers) -- v. 522. Contributions Yang, Chung-Chun, 1942- LC Classifications QA331 .H78 2000 Pagination viii, 295 p. ; Number of Pages 295 Open Library OL20001558M ISBN 10 0792365321 LC Control Number 00060523

Idea. Non-archimedean geometry is geometry over non-archimedean fields. While the concrete results are quite different, the basic formalism of algebraic schemes and formal schemes over a non-archimedean field K K is the special case of the standard formalism over any field. The “correct” analytic geometry over non-archimedean field, however, is not a straightforward analogue of the complex.

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### Meromorphic functions over non-archimedean fields by Pei-Chu Hu Download PDF EPUB FB2

Get this from a library. Meromorphic functions over non-archimedean fields. [Pei-Chu Hu; Chung-Chun Yang] -- "This book introduces value distribution theory over non-Archimedean fields starting with a survey of two Nevanlinna-type main theorems and defect relations for.

Get this from a library. Meromorphic Functions over Non-Archimedean Fields. [Pei-Chu Hu; Chung-Chun Yang] -- This book introduces value distribution theory over non-Archimedean fields, starting with a survey of two Nevanlinna-type main theorems and defect relations for.

Meromorphic Functions over Non-Archimedean Fields. Authors: Pei-Chu Hu, Chung-Chun Yang Free Preview. 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.

Meromorphic Functions Over Non-Archimedean Fields by Pei-Chu Hu and Chung-Chun Yang Overview - 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.

Abstract. In this paper, we give some conditions to assure that the equation P(X)=Q(Y) has no meromorphic solutions in all K, where P and Q are polynomials over an algebraically closed field K of characteristic Meromorphic functions over non-archimedean fields book, complete with respect to a non-Archimedean valuation.

In particular, if P and Q satisfy the hypothesis (F) introduced by H. Fujimoto, a necessary and sufficient condition is Cited by: 6. Meromorphic Functions Over Non-Archimedean Fields 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.

Non-Archimedean case. The following table lists the analogous state of affairs in the p-adic case. We denote by C p the completion of an algebraic closure of the field of p-adic numbers.

By A p (X) and M p (X) we denote respectively the ring of analytic functions and Cited by: Meromorphic functions over non-archimedean fields book. Q (Y) has no meromorphic solutions in all K, where P and Q are polynomials over an algebraically closed ﬁeld K of characteristic zero, complete with respect to a non- Archimedean valuation.

Download Meromorphic Functions And Analytic Curves ebook PDF or Read Online books Meromorphic Functions Over Non Archimedean Fields.

Author: Pei-Chu Hu ISBN: Genre: Mathematics In this book, we will introduce non-Archimedean analogues of Nevanlinna theory and its applications.

In value distribution theory, the main. non archimedean functional analysis Download non archimedean functional analysis or read online books in PDF, EPUB, Tuebl, and Mobi Format. Click Download or Read Online button to get non archimedean functional analysis book now.

This site is like a library, Use search box. In mathematics, a non-Archimedean ordered field is an ordered field that does not satisfy the Archimedean es are the Levi-Civita field, the hyperreal numbers, the surreal numbers, the Dehn field, and the field of rational functions with real coefficients with a suitable order.

Definition. The Archimedean property is a property of certain ordered fields such as the rational Formalizations: Differentials, Hyperreal numbers, Dual. 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.

Value sharing problems for differential and difference polynomials of meromorphic functions in a non-Archimedean field January P-Adic Numbers Ultrametric Analysis and Applications 9(1) I'm looking for good textbooks on analytic functions on Banach spaces over a non-Archimedean field.

If you know one(s), please let me know. Meromorphic functions 69 Chapter 4. Analytic Curves 75 One-dimensional quasipolyhedra 75 book is devoted to the study of these analytic spaces.

We try to show that V. Berkovich, Spectral theory and analytic geometry over non-Archimedean fields II, Preprint IHES/M/88/43, September File Size: 2MB. In abstract algebra and analysis, the Archimedean property, named after the ancient Greek mathematician Archimedes of Syracuse, is a property held by some algebraic structures, such as ordered or normed groups, and y speaking, it is the property of having no infinitely large or infinitely small elements.

It was Otto Stolz who gave the axiom of Archimedes its name because it. meromorphic function[¦merə¦mȯrfik ′fəŋkshən] (mathematics) A function of complex variables which is analytic in its domain of definition save at a finite number of points which are poles.

Meromorphic Function a function that can be represented in the form of a quotient of two entire functions, that is, the quotient of the sums of two. Katsaras -- Linear topologies on non-Archimedean function spaces; A.

Katsaras, L. Khan, and A. Khan -- On maximal closed ideals in topological algebras of continuous vector-valued functions over non-Archimedean valued fields. DOWNLOAD NOW» Articles included in this book feature recent developments in various areas of non-Archimedean analysis: summation of -adic series, rational maps on the projective line over, non-Archimedean Hahn-Banach theorems, ultrametric Calkin algebras, -modules with a convex base, non-compact Trace class operators and Schatten-class operators in -adic Hilbert spaces, algebras of.

"Non-Archimedean Field" is a term used to refer to a non-Archimedean valued field or a non-Archimedean ordered field. Of course, this term is used within a context that allows you to decide whether we are treating with the former or latter case.

Now I am going to define these two concepts. Articles included in this book feature recent developments in various areas of non-Archimedean analysis: summation of -adic series, rational maps on the projective line over, non-Archimedean Hahn-Banach theorems, ultrametric Calkin algebras, -modules with a convex base, non-compact Trace class operators and Schatten-class operators in -adic.

Meromorphic Functions Over Non-Archimedean Fields Finite or Infinite Dimensional Complex Analysis and Applications (Advances in Complex Analysis and Its. The Paperback of the Advances in Ultrametric Analysis by Khodr Shamseddine at Barnes & Noble.

FREE Shipping on \$35 or more. Due to COVID, orders may be delayed. Analytic Functions over Non-Archimedean Fields Classical rigid geometry may be viewed as a theory of analytic functions over local ﬁelds or, more generally, over ﬁelds that are complete under a non-Archimedean absolute value; complete means that every Cauchy sequence is converging.

For example, choosing a prime p, the ﬁeld QFile Size: 3MB. 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.

Discover Book Depository's huge selection of Yang Chung Chun books online. Free delivery worldwide on over 20 million titles. This book is the first to be devoted to the theory of vector-valued functions with one variable. This theory is one of the fundamental tools employed in modern physics, the spectral theory of operators, approximation of analytic operators, analytic mappings between vectors, and vector-valued functions of several variables.

The book contains three chapters devoted to the theory of normal. Intended for graduate courses or for independent study, this book presents the basic theory of fields. The first part begins with a discussion of polynomials over a ring, the division algorithm, irreducibility, field extensions, and embeddings.

The second part is devoted to Galois theory. The third part of the book treats the theory of binomials. This is probably the first book dedicated to this topic.

The behaviour of the analytic elements on an infraconnected set D in K an algebraically closed complete ultrametric field is mainly explained by the circular filters and the monotonous filters on D, especially the T-filters: zeros of the elements, Mittag-Leffler series, factorization, Motzkin factorization, maximum principle, injectivity.

Example Let F be a non-Archimedean local ﬁeld. The group G = GL n(F) is unimodular. (In general a reductive p-adic group is unimodular.) This may be seen as follows. Note that ∆ G is trivial on [G,G] as the range of ∆ G is abelian. Further by the deﬁning relation ∆ G is trivial on the centre Z.

(Both these remarks are true for any File Size: KB. Analytic Functions - Ebook written by Lars Valerian Ahlfors. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Analytic Functions. The articles included in this book feature recent developments in various areas of non-archimedean analysis: branched values and zeros of the derivative of a $$p$$-adic meromorphic function, $$p$$-adic meromorphic functions $$f^{\prime}P^{\prime}(f), g^{\prime}P^{\prime}(g)$$ sharing a small function, properties of composition of analytic.

Idea. An archimedean field is an ordered field in which every element is bounded above by a natural number.

So an archimedean field has no infinite elements (and thus no non-zero infinitesimal elements). Non-archimedean fields. For k k a non-archimedean field for some non-archimedean absolute value | − | {\vert -\vert} one defines. its ring of integers to be. Meromorphic functions over Non-Archimedean fields (P.C.

Hu & C.C. Yang), Kluwer Academic Publishers, 7. Factorization theory of meromorphic function, Lecture Notes in pure and applied mathematics (edited by C.C. Yang), Vol. 78, Marcel Dekker, 8.

The Skeleton of the Jacobian, the Jacobian of the Skeleton, and Lifting Meromorphic Functions From Tropical to Algebraic Curves Matthew Baker School of Mathematics, Georgia Institute of Technology, Atlanta, GAUSACited by: I was wondering could anyone tell me a reference for the fact that an absolutely quasi-simple algebraic group over a non-archimedean local field which is centreless and non-compact acts faithfully and Weyl transitively on a regular locally finite building, and its image in the automorphism group is closed in the compact-open topology.

The book also presents the state of the art in the studies of the analogues between Diophantine approximation (in number theory) and value distribution theory (in complex analysis), with a method based on Vojta’s dictionary for the terms of these two fields.

The approaches are relatively natural and more effective than existing methods. Destination page number Search scope Search Text Search scope Search Text. In this context, complete means "order complete" rather than complete in the sense of metric spaces.

A non-archimedian ordered field will necessarily have infinitely small elements, so I suspect that if you try to impose a metric you'll get something pathological like the. Proposition () The function j¢jp is a non-archimedean valuation on Q.

Moreover, we have the following (cf. [?, p]): Theorem (). Let A be the image of the usual homomorphism Z! |. An absolute value j¢j is non-archimedean if and only if jaj • 1 for all a 2 A.

In particular, an absolute value on Qis non-archimedean if and only if jnj.Non-Archimedean functional analysis, [Rooij, A. C. M. van] on *FREE* shipping on qualifying offers. Non-Archimedean functional analysis5/5(1).Ta Thi Hoai An, A.

Escassut, Meromorphic solutions of equations over non-Archimedean fields, Ramanujan J. 15 (), N0 3, - 18 Ta Thi Hoai An, J. T.-Y. Wang and P.-M. Wong, Non-Archimedean analytic curves in the complements of hypersurface divisors.