Studies On Shared Values Of Meromorphic Functions

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Studies On Shared Values Of Meromorphic Functions

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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.

Uniqueness Theory Of Meromorphic Functions

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Author : Chung-Chun Yang
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-10-04

Uniqueness Theory Of Meromorphic Functions written by Chung-Chun Yang 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 2004-10-04 with Mathematics categories.

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book systematically summarizes the most important results in the field, including many of the authors' own previously unpublished results.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.

Unicity Of Meromorphic Mappings

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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.

Uniqueness And Value Sharing Of Meromorphic Functions

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Author : Ping Li
language : en
Publisher:
Release Date : 1996

Uniqueness And Value Sharing Of Meromorphic Functions written by Ping Li and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Functions, Meromorphic categories.

Studies On The Value Distribution Of Meromorphic Functions

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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.

Entire And Meromorphic Functions

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Author : Lee A. Rubel
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Entire And Meromorphic Functions written by Lee A. Rubel 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 2012-12-06 with Mathematics categories.

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.

Factorization Of Meromophic Functions

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Author : United States. Naval Research Office
language : en
Publisher:
Release Date : 1972

Factorization Of Meromophic Functions written by United States. Naval Research Office and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Factors (Algebra) categories.

Value Distribution Of Meromorphic Functions

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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.

Value Distribution Of L Functions

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Author : Jörn Steuding
language : en
Publisher: Springer
Release Date : 2007-05-26

Value Distribution Of L Functions written by Jörn Steuding and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-26 with Mathematics categories.

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.

Proceedings Of The Second Isaac Congress

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Author : Heinrich G.W. Begehr
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01

Proceedings Of The Second Isaac Congress written by Heinrich G.W. Begehr 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 2013-12-01 with Mathematics categories.

This book is the Proceedings of the Second ISAAC Congress. ISAAC is the acronym of the International Society for Analysis, its Applications and Computation. The president of ISAAC is Professor Robert P. Gilbert, the second named editor of this book, e-mail: [email protected]. The Congress is world-wide valued so highly that an application for a grant has been selected and this project has been executed with Grant No. 11-56 from *the Commemorative Association for the Japan World Exposition (1970). The finance of the publication of this book is exclusively the said Grant No. 11-56 from *. Thus, a pair of each one copy of two volumes of this book will be sent to all contributors, who registered at the Second ISAAC Congress in Fukuoka, free of charge by the Kluwer Academic Publishers. Analysis is understood here in the broad sense of the word, includ ing differential equations, integral equations, functional analysis, and function theory. It is the purpose of ISAAC to promote analysis, its applications, and its interaction with computation. With this objective, ISAAC organizes international Congresses for the presentation and dis cussion of research on analysis. ISAAC welcomes new members and those interested in joining ISAAC are encouraged to look at the web site http://www .math. udel.edu/ gilbert/isaac/index.html vi and http://www.math.fu-berlin.de/ rd/ ag/isaac/newton/index.html.