Nevanlinna S Theory Of Value Distribution
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Nevanlinna S Theory Of Value Distribution
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Author : William Cherry
language : en
Publisher:
Release Date : 2014-01-15
Nevanlinna S Theory Of Value Distribution written by William Cherry and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Nevanlinna S Theory Of Value Distribution
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Author : William Cherry
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Nevanlinna S Theory Of Value Distribution written by William Cherry and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
This monograph serves as a self-contained introduction to Nevanlinna's theory of value distribution as well as a valuable reference for research specialists. Authors present, for the first time in book form, the most modern and refined versions of the Second Main Theorem with precise error terms, in both the geometric and logarithmic derivative based approaches. A unique feature of the monograph is its number theoretic digressions These special sections assume no background in number theory and explore the exciting interconnections between Nevanlinna theory and the theory of Diophantine approximation.
Value Distribution Theory
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Author : L. Sario
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Value Distribution Theory written by L. Sario and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
The purpose of this research monograph is to build up a modern value distribution theory for complex analytic mappings between abstract Riemann surfaces. All results presented herein are new in that, apart from the classical background material in the last chapter, there is no over lapping with any existing monograph on merom orphic functions. Broadly speaking the division of the book is as follows: The Introduction and Chapters I to III deal mainly with the theory of mappings of arbitrary Riemann surfaces as developed by the first named author; Chapter IV, due to Nakai, is devoted to meromorphic functions on parabolic surfaces; Chapter V contains Matsumoto's results on Picard sets; Chapter VI, pre dominantly due to the second named author, presents the so-called nonintegrated forms of the main theorems and includes some joint work by both authors. For a complete list of writers whose results have been discussed we refer to the Author Index.
Value Distribution Theory And Related Topics
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Author : Grigor A. Barsegian
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-02
Value Distribution Theory And Related Topics written by Grigor A. Barsegian and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-05-02 with Mathematics categories.
The Nevanlinna theory of value distribution of meromorphic functions, one of the milestones of complex analysis during the last century, was c- ated to extend the classical results concerning the distribution of of entire functions to the more general setting of meromorphic functions. Later on, a similar reasoning has been applied to algebroid functions, subharmonic functions and meromorphic functions on Riemann surfaces as well as to - alytic functions of several complex variables, holomorphic and meromorphic mappings and to the theory of minimal surfaces. Moreover, several appli- tions of the theory have been exploited, including complex differential and functional equations, complex dynamics and Diophantine equations. The main emphasis of this collection is to direct attention to a number of recently developed novel ideas and generalizations that relate to the - velopment of value distribution theory and its applications. In particular, we mean a recent theory that replaces the conventional consideration of counting within a disc by an analysis of their geometric locations. Another such example is presented by the generalizations of the second main theorem to higher dimensional cases by using the jet theory. Moreover, s- ilar ideas apparently may be applied to several related areas as well, such as to partial differential equations and to differential geometry. Indeed, most of these applications go back to the problem of analyzing zeros of certain complex or real functions, meaning in fact to investigate level sets or level surfaces.
Value Distribution Theory
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Author : Yang Lo
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Value Distribution Theory written by Yang Lo and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
It is well known that solving certain theoretical or practical problems often depends on exploring the behavior of the roots of an equation such as (1) J(z) = a, where J(z) is an entire or meromorphic function and a is a complex value. It is especially important to investigate the number n(r, J = a) of the roots of (1) and their distribution in a disk Izl ~ r, each root being counted with its multiplicity. It was the research on such topics that raised the curtain on the theory of value distribution of entire or meromorphic functions. In the last century, the famous mathematician E. Picard obtained the pathbreaking result: Any non-constant entire function J(z) must take every finite complex value infinitely many times, with at most one excep tion. Later, E. Borel, by introducing the concept of the order of an entire function, gave the above result a more precise formulation as follows. An entire function J (z) of order A( 0 A
Value Distribution Theory Related To Number Theory
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Author : Pei-Chu Hu
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-10-06
Value Distribution Theory Related To Number Theory written by Pei-Chu Hu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-10-06 with Mathematics categories.
The subject of the book is Diophantine approximation and Nevanlinna theory. This book proves not just some new results and directions but challenging open problems in Diophantine approximation and Nevanlinna theory. The authors’ newest research activities on these subjects over the past eight years are collected here. Some of the significant findings are the proof of Green-Griffiths conjecture by using meromorphic connections and Jacobian sections, generalized abc-conjecture, and more.
Value Distribution Theory For Meromorphic Maps
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Author : Wilhelm Stoll
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Value Distribution Theory For Meromorphic Maps written by Wilhelm Stoll and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Science categories.
Value distribution theory studies the behavior of mermorphic maps. Let f: M - N be a merom orphic map between complex manifolds. A target family CI ~ (Ea1aEA of analytic subsets Ea of N is given where A is a connected. compact complex manifold. The behavior of the inverse 1 family ["'(CI) = (f- {E )laEA is investigated. A substantial theory has been a created by many contributors. Usually the targets Ea stay fixed. However we can consider a finite set IJ of meromorphic maps g : M - A and study the incidence f{z) E Eg(z) for z E M and some g E IJ. Here we investigate this situation: M is a parabolic manifold of dimension m and N = lP n is the n-dimensional projective space. The family of hyperplanes in lP n is the target family parameterized by the dual projective space lP* We obtain a Nevanlinna theory consisting of several n First Main Theorems. Second Main Theorems and Defect Relations and extend recent work by B. Shiffman and by S. Mori. We use the Ahlfors-Weyl theory modified by the curvature method of Cowen and Griffiths. The Introduction consists of two parts. In Part A. we sketch the theory for fixed targets to provide background for those who are familar with complex analysis but are not acquainted with value distribution theory.
Tropical Value Distribution Theory And Ultra Discrete Equations
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Author : Risto Korhonen
language : en
Publisher: World Scientific
Release Date : 2015-03-17
Tropical Value Distribution Theory And Ultra Discrete Equations written by Risto Korhonen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-17 with Mathematics categories.
This is the first textbook-type presentation of tropical value distribution theory. It provides a detailed introduction of the tropical version of the Nevanlinna theory, describing growth and value distribution analysis of continuous, piecewise linear functions on the real axis. The book also includes applications of this theory to ultra-discrete equations. Three appendices are given to compare the contents of the theory with the classical counterparts in complex analysis. Detailed presentation of the proofs makes the book accessible for lecture courses and independent studies at the graduate and post-doctoral level. Contents:Tropical Polynomials, Rationals and ExponentialsTropical Entire FunctionsOne-dimensional Tropical Nevanlinna TheoryClunie and Mohon'ko Type TheoremsTropical Holomorphic CurvesRepresentations of Tropical Periodic FunctionsApplications to Ultra-Discrete EquationsAppendices:Classical Nevanlinna and Cartan TheoriesIntroduction to Ultra-Discrete Painlevé EquationsSome Operators in Complex Analysis Readership: Graduate students, post-graduates and researchers. Key Features:First monograph type presentation in this topicSome of the material is new in contents, which follows in the presentationThe contributors have been active in value distribution theory, including its tropical variantKeywords:Tropical Mathematics;Value Distribution Theory;Ultra-discrete Equations
Value Distribution Theory
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Author : Le Yang
language : en
Publisher: Springer
Release Date : 1993
Value Distribution Theory written by Le Yang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
Ricardo And The Theory Of Value Distribution And Growth
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Author : Giovanni A. Caravale
language : en
Publisher: Routledge
Release Date : 2013-04-15
Ricardo And The Theory Of Value Distribution And Growth written by Giovanni A. Caravale and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-15 with Business & Economics categories.
The book presents a rigorous reconstruction of Ricardo's contribution to economic theory and a unifying interpretation of the key issues of Ricardo's research. Part One deals primarily with the problems of value and distribution Part Two deals specifically with the issues of distribution and growth. * Contemporary economic literature in the fields of value, distribution and growth is witnessing a renewed interest in the approach of the classical school, notably in the work of David Ricardo.