Value Distribution Of Meromorphic Functions

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Value Distribution of Meromorphic Functions

Author : Jianhua Zheng
Publisher : Springer Science & Business Media
ISBN 13 : 3642129099
Total Pages : 315 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Value Distribution of Meromorphic Functions by : Jianhua Zheng

Download or read book Value Distribution of Meromorphic Functions written by Jianhua Zheng and published by Springer Science & Business Media. This book was released on 2011-03-31 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.

Value Distribution of Meromorphic Functions

Author : Anatoliĭ Asirovich Golʹdberg
Publisher : American Mathematical Soc.
ISBN 13 : 9780821889718
Total Pages : 512 pages
Book Rating : 4.8/5 (897 download)

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Book Synopsis Value Distribution of Meromorphic Functions by : Anatoliĭ Asirovich Golʹdberg

Download or read book Value Distribution of Meromorphic Functions written by Anatoliĭ Asirovich Golʹdberg and published by American Mathematical Soc.. This book was released on with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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 of Meromorphic Functions

Author : Anatoliĭ Asirovich Golʹdberg
Publisher : American Mathematical Soc.
ISBN 13 : 9780821842652
Total Pages : 488 pages
Book Rating : 4.8/5 (426 download)

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Book Synopsis Value Distribution of Meromorphic Functions by : Anatoliĭ Asirovich Golʹdberg

Download or read book Value Distribution of Meromorphic Functions written by Anatoliĭ Asirovich Golʹdberg and published by American Mathematical Soc.. This book was released on 2008 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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

Author : L. Sario
Publisher : Springer Science & Business Media
ISBN 13 : 1461581265
Total Pages : 247 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Value Distribution Theory by : L. Sario

Download or read book Value Distribution Theory written by L. Sario and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Yang Lo
Publisher : Springer Science & Business Media
ISBN 13 : 3662029154
Total Pages : 280 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Value Distribution Theory by : Yang Lo

Download or read book Value Distribution Theory written by Yang Lo and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Entire and Meromorphic Functions

Author : Lee A. Rubel
Publisher : Springer Science & Business Media
ISBN 13 : 1461207355
Total Pages : 196 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Entire and Meromorphic Functions by : Lee A. Rubel

Download or read book Entire and Meromorphic Functions written by Lee A. Rubel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics is a beautiful subject, and entire functions is its most beautiful branch. Every aspect of mathematics enters into it, from analysis, algebra, and geometry all the way to differential equations and logic. For example, my favorite theorem in all of mathematics is a theorem of R. NevanJinna that two functions, meromorphic in the whole complex plane, that share five values must be identical. For real functions, there is nothing that even remotely corresponds to this. This book is an introduction to the theory of entire and meromorphic functions, with a heavy emphasis on Nevanlinna theory, otherwise known as value-distribution theory. Things included here that occur in no other book (that we are aware of) are the Fourier series method for entire and mero morphic functions, a study of integer valued entire functions, the Malliavin Rubel extension of Carlson's Theorem (the "sampling theorem"), and the first-order theory of the ring of all entire functions, and a final chapter on Tarski's "High School Algebra Problem," a topic from mathematical logic that connects with entire functions. This book grew out of a set of classroom notes for a course given at the University of Illinois in 1963, but they have been much changed, corrected, expanded, and updated, partially for a similar course at the same place in 1993. My thanks to the many students who prepared notes and have given corrections and comments.

Value Distribution Theory for Meromorphic Maps

Author : Wilhelm Stoll
Publisher : Springer Science & Business Media
ISBN 13 : 3663052923
Total Pages : 358 pages
Book Rating : 4.6/5 (63 download)

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Book Synopsis Value Distribution Theory for Meromorphic Maps by : Wilhelm Stoll

Download or read book Value Distribution Theory for Meromorphic Maps written by Wilhelm Stoll and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 and Related Topics

Author : Grigor A. Barsegian
Publisher : Springer Science & Business Media
ISBN 13 : 1402079516
Total Pages : 333 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Value Distribution Theory and Related Topics by : Grigor A. Barsegian

Download or read book Value Distribution Theory and Related Topics written by Grigor A. Barsegian and published by Springer Science & Business Media. This book was released on 2006-05-02 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Uniqueness Theory of Meromorphic Functions

Author : Chung-Chun Yang
Publisher : Springer Science & Business Media
ISBN 13 : 9781402014482
Total Pages : 590 pages
Book Rating : 4.0/5 (144 download)

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Book Synopsis Uniqueness Theory of Meromorphic Functions by : Chung-Chun Yang

Download or read book Uniqueness Theory of Meromorphic Functions written by Chung-Chun Yang and published by Springer Science & Business Media. This book was released on 2004-10-04 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first monograph in the field of uniqueness theory of meromorphic functions dealing with conditions under which there is the unique function satisfying given hypotheses. Developed by R. Nevanlinna, a Finnish mathematician, early in the 1920's, research in the field has developed rapidly over the past three decades with a great deal of fruitful results. This book systematically summarizes the most important results in the field, including many of the authors' own previously unpublished results. In addition, useful skills and simple proofs are introduced. This book is suitable for higher level and graduate students who have a basic grounding in complex analysis, but will also appeal to researchers in mathematics.

Meromorphic Functions over non-Archimedean Fields

Author : Pei-Chu Hu
Publisher : Springer Science & Business Media
ISBN 13 : 9780792365327
Total Pages : 308 pages
Book Rating : 4.3/5 (653 download)

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Book Synopsis Meromorphic Functions over non-Archimedean Fields by : Pei-Chu Hu

Download or read book Meromorphic Functions over non-Archimedean Fields written by Pei-Chu Hu and published by Springer Science & Business Media. This book was released on 2000-09-30 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 and holomorphic curves. Secondly, it gives applications of the above theory to, e.g., abc-conjecture, Waring's problem, uniqueness theorems for meromorphic functions, and Malmquist-type theorems for differential equations over non-Archimedean fields. Next, iteration theory of rational and entire functions over non-Archimedean fields and Schmidt's subspace theorems are studied. Finally, the book suggests some new problems for further research. Audience: This work will be of interest to graduate students working in complex or diophantine approximation as well as to researchers involved in the fields of analysis, complex function theory of one or several variables, and analytic spaces.

Unicity of Meromorphic Mappings

Author : Pei-Chu Hu
Publisher : Springer Science & Business Media
ISBN 13 : 1475737750
Total Pages : 472 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Unicity of Meromorphic Mappings by : Pei-Chu Hu

Download or read book Unicity of Meromorphic Mappings written by Pei-Chu Hu and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Studies on the value distribution of meromorphic functions

Author : Liisa Kinnunen
Publisher :
ISBN 13 : 9789517086059
Total Pages : 26 pages
Book Rating : 4.0/5 (86 download)

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Book Synopsis Studies on the value distribution of meromorphic functions by : Liisa Kinnunen

Download or read book Studies on the value distribution of meromorphic functions written by Liisa Kinnunen and published by . This book was released on 1998 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Value-Distribution of L-Functions

Author : Jörn Steuding
Publisher : Springer
ISBN 13 : 3540448225
Total Pages : 322 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Value-Distribution of L-Functions by : Jörn Steuding

Download or read book Value-Distribution of L-Functions written by Jörn Steuding and published by Springer. This book was released on 2007-05-26 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes present recent results in the value-distribution theory of L-functions with emphasis on the phenomenon of universality. Universality has a strong impact on the zero-distribution: Riemann’s hypothesis is true only if the Riemann zeta-function can approximate itself uniformly. The text proves universality for polynomial Euler products. The authors’ approach follows mainly Bagchi's probabilistic method. Discussion touches on related topics: almost periodicity, density estimates, Nevanlinna theory, and functional independence.

Radical Distribution and Deficiencies of the Values of a Meromorphic Function

Author : Albert Edrei
Publisher :
ISBN 13 :
Total Pages : 64 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Radical Distribution and Deficiencies of the Values of a Meromorphic Function by : Albert Edrei

Download or read book Radical Distribution and Deficiencies of the Values of a Meromorphic Function written by Albert Edrei and published by . This book was released on 1960 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nevanlinna’s Theory of Value Distribution

Author : William Cherry
Publisher : Springer Science & Business Media
ISBN 13 : 9783540664161
Total Pages : 224 pages
Book Rating : 4.6/5 (641 download)

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Book Synopsis Nevanlinna’s Theory of Value Distribution by : William Cherry

Download or read book Nevanlinna’s Theory of Value Distribution written by William Cherry and published by Springer Science & Business Media. This book was released on 2001-04-24 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Theory of Entire and Meromorphic Functions

Author : Guan-hou Zhang
Publisher : American Mathematical Soc.
ISBN 13 : 9780821887646
Total Pages : 394 pages
Book Rating : 4.8/5 (876 download)

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Book Synopsis Theory of Entire and Meromorphic Functions by : Guan-hou Zhang

Download or read book Theory of Entire and Meromorphic Functions written by Guan-hou Zhang and published by American Mathematical Soc.. This book was released on 1993-01-01 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book was originally written in Chinese in 1986 by the noted complex analyst Zhang Guan-Hou, who was a research fellow at the Academia Sinica. The book provides a basic introduction to the development of the theory of entire and meromorphic functions from the 1950s to the early 1980s. After an opening chapter introducing fundamentals of Nevanlinna's value distribution theory, this book discusses various relationships among and developments of three central concepts: deficient value, asymptotic value, and singular direction. This book describes many significant results and research directions developed by Zhang and other Chinese complex analysts and published in Chinese mathematical journals. A comprehensive and self-contained reference, this book is useful for graduate students and researchers in complex analysis.

Value Distribution Theory

Author : Yang Lo
Publisher : Springer
ISBN 13 : 9783540543794
Total Pages : 269 pages
Book Rating : 4.5/5 (437 download)

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Book Synopsis Value Distribution Theory by : Yang Lo

Download or read book Value Distribution Theory written by Yang Lo and published by Springer. This book was released on 1993-11-09 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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