Studies On The Value Distribution Of Meromorphic Functions

DOWNLOAD

Download Studies On The Value Distribution Of Meromorphic Functions PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Studies On The Value Distribution Of Meromorphic Functions book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Studies On The Value Distribution Of Meromorphic Functions

DOWNLOAD
Author : Liisa Kinnunen
language : en
Publisher:
Release Date : 1998

Studies On The Value Distribution Of Meromorphic Functions written by Liisa Kinnunen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Functions, Meromorphic categories.

Value Distribution Theory For Meromorphic Maps

DOWNLOAD
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.

Value Distribution Theory

DOWNLOAD
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 Of Meromorphic Functions

DOWNLOAD
Author : Anatoliĭ Asirovich Golʹdberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2008

Value Distribution Of Meromorphic Functions written by Anatoliĭ Asirovich Golʹdberg and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.

"This book contains a comprehensive exposition of the Nevanlinna theory of meromorphic functions of one complex variable, with detailed study of deficiencies, value distribution, and asymptotic properties of meromorphic functions." "The main body of the book is a translation of the Russian original published in 1970, which has been one of the most popular sources in this field since then. New references and footnotes related to recent achievements in the topics considered in the original edition have been added and a few corrections made. A new Appendix with a survey of the results obtained after 1970 and extensive bibliography has been written by Alexandre Ermenko and James K. Langley for this English edition." "The only prerequisite for understanding material of this book is an undergraduate course in the theory of functions of one complex variable."--BOOK JACKET.

Value Distribution Theory

DOWNLOAD
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.

Studies On Shared Values Of Meromorphic Functions

DOWNLOAD
Author : Jilong Zhang
language : en
Publisher:
Release Date : 2008

Studies On Shared Values Of Meromorphic Functions written by Jilong Zhang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Functions, Meromorphic categories.

This survey part of the thesis contains some background to the series of studies on shared values of meromorphic functions. Nevanlinna's value distribution theory and some classical results are introduced. Meromorphic functions sharing values with their derivatives and two differential polynomials sharing one small function are studied. A short summary of the articles is included.

Radial Cluster Sets And The Distribution Of Values Of Meromorphic Functions

DOWNLOAD
Author : William Blauvelet Woolf
language : en
Publisher:
Release Date : 1959

Radial Cluster Sets And The Distribution Of Values Of Meromorphic Functions written by William Blauvelet Woolf and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1959 with Functions, Meromorphic categories.

Value Distribution Theory

DOWNLOAD
Author : Yang Lo
language : en
Publisher: Springer
Release Date : 1993-11-09

Value Distribution Theory written by Yang Lo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-11-09 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

Unicity Of Meromorphic Mappings

DOWNLOAD
Author : Pei-Chu Hu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18

Unicity Of Meromorphic Mappings 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 2013-04-18 with Mathematics categories.

For a given meromorphic function I(z) and an arbitrary value a, Nevanlinna's value distribution theory, which can be derived from the well known Poisson-Jensen for mula, deals with relationships between the growth of the function and quantitative estimations of the roots of the equation: 1 (z) - a = O. In the 1920s as an application of the celebrated Nevanlinna's value distribution theory of meromorphic functions, R. Nevanlinna [188] himself proved that for two nonconstant meromorphic func tions I, 9 and five distinctive values ai (i = 1,2,3,4,5) in the extended plane, if 1 1- (ai) = g-l(ai) 1M (ignoring multiplicities) for i = 1,2,3,4,5, then 1 = g. Fur 1 thermore, if 1- (ai) = g-l(ai) CM (counting multiplicities) for i = 1,2,3 and 4, then 1 = L(g), where L denotes a suitable Mobius transformation. Then in the 19708, F. Gross and C. C. Yang started to study the similar but more general questions of two functions that share sets of values. For instance, they proved that if 1 and 9 are two nonconstant entire functions and 8 , 82 and 83 are three distinctive finite sets such 1 1 that 1- (8 ) = g-1(8 ) CM for i = 1,2,3, then 1 = g.

Value Distribution Of Meromorphic Functions

DOWNLOAD
Author : Jianhua Zheng
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-03-31

Value Distribution Of Meromorphic Functions written by Jianhua Zheng 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 2011-03-31 with Mathematics categories.

"Value Distribution of Meromorphic Functions" focuses on functions meromorphic in an angle or on the complex plane, T directions, deficient values, singular values, potential theory in value distribution and the proof of the celebrated Nevanlinna conjecture. The book introduces various characteristics of meromorphic functions and their connections, several aspects of new singular directions, new results on estimates of the number of deficient values, new results on singular values and behaviours of subharmonic functions which are the foundation for further discussion on the proof of the Nevanlinna conjecture. The independent significance of normality of subharmonic function family is emphasized. This book is designed for scientists, engineers and post graduated students engaged in Complex Analysis and Meromorphic Functions. Dr. Jianhua Zheng is a Professor at the Department of Mathematical Sciences, Tsinghua University, China.