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: Springer Science & Business Media
Release Date : 2001-04-24
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 2001-04-24 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 : 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
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.
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.
Nevanlinna Theory Normal Families And Algebraic Differential Equations
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Author : Norbert Steinmetz
language : en
Publisher: Springer
Release Date : 2017-07-24
Nevanlinna Theory Normal Families And Algebraic Differential Equations written by Norbert Steinmetz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-24 with Mathematics categories.
This book offers a modern introduction to Nevanlinna theory and its intricate relation to the theory of normal families, algebraic functions, asymptotic series, and algebraic differential equations. Following a comprehensive treatment of Nevanlinna’s theory of value distribution, the author presents advances made since Hayman’s work on the value distribution of differential polynomials and illustrates how value- and pair-sharing problems are linked to algebraic curves and Briot–Bouquet differential equations. In addition to discussing classical applications of Nevanlinna theory, the book outlines state-of-the-art research, such as the effect of the Yosida and Zalcman–Pang method of re-scaling to algebraic differential equations, and presents the Painlevé–Yosida theorem, which relates Painlevé transcendents and solutions to selected 2D Hamiltonian systems to certain Yosida classes of meromorphic functions. Aimed at graduate students interested in recent developments in the field and researchers working on related problems, Nevanlinna Theory, Normal Families, and Algebraic Differential Equations will also be of interest to complex analysts looking for an introduction to various topics in the subject area. With examples, exercises and proofs seamlessly intertwined with the body of the text, this book is particularly suitable for the more advanced reader.
Nevanlinna Theory In Several Complex Variables And Diophantine Approximation
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Author : Junjiro Noguchi
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-09
Nevanlinna Theory In Several Complex Variables And Diophantine Approximation written by Junjiro Noguchi 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 2013-12-09 with Mathematics categories.
The aim of this book is to provide a comprehensive account of higher dimensional Nevanlinna theory and its relations with Diophantine approximation theory for graduate students and interested researchers. This book with nine chapters systematically describes Nevanlinna theory of meromorphic maps between algebraic varieties or complex spaces, building up from the classical theory of meromorphic functions on the complex plane with full proofs in Chap. 1 to the current state of research. Chapter 2 presents the First Main Theorem for coherent ideal sheaves in a very general form. With the preparation of plurisubharmonic functions, how the theory to be generalized in a higher dimension is described. In Chap. 3 the Second Main Theorem for differentiably non-degenerate meromorphic maps by Griffiths and others is proved as a prototype of higher dimensional Nevanlinna theory. Establishing such a Second Main Theorem for entire curves in general complex algebraic varieties is a wide-open problem. In Chap. 4, the Cartan-Nochka Second Main Theorem in the linear projective case and the Logarithmic Bloch-Ochiai Theorem in the case of general algebraic varieties are proved. Then the theory of entire curves in semi-abelian varieties, including the Second Main Theorem of Noguchi-Winkelmann-Yamanoi, is dealt with in full details in Chap. 6. For that purpose Chap. 5 is devoted to the notion of semi-abelian varieties. The result leads to a number of applications. With these results, the Kobayashi hyperbolicity problems are discussed in Chap. 7. In the last two chapters Diophantine approximation theory is dealt with from the viewpoint of higher dimensional Nevanlinna theory, and the Lang-Vojta conjecture is confirmed in some cases. In Chap. 8 the theory over function fields is discussed. Finally, in Chap. 9, the theorems of Roth, Schmidt, Faltings, and Vojta over number fields are presented and formulated in view of Nevanlinna theory with results motivated by those in Chaps. 4, 6, and 7.
Diophantine Approximations And Value Distribution Theory
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Author : Paul Alan Vojta
language : en
Publisher: Springer
Release Date : 2006-11-15
Diophantine Approximations And Value Distribution Theory written by Paul Alan Vojta and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Analysis And Mathematical Physics
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Author : Shaun Bullett
language : en
Publisher: World Scientific
Release Date : 2016-12-22
Analysis And Mathematical Physics written by Shaun Bullett and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-22 with Science categories.
This is a concise reference book on analysis and mathematical physics, leading readers from a foundation to advanced level understanding of the topic. This is the perfect text for graduate or PhD mathematical-science students looking for support in topics such as distributions, Fourier transforms and microlocal analysis, C* Algebras, value distribution of meromorphic functions, noncommutative differential geometry, differential geometry and mathematical physics, mathematical problems of general relativity, and special functions of mathematical physics.Analysis and Mathematical Physics is the sixth volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Edited by the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas.
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.
On the one hand, this monograph serves as a self-contained introduction to Nevanlinna's theory of value distribution because the authors only assume the reader is familiar with the basics of complex analysis. On the other hand, the monograph also serves as a valuable reference for the research specialist because the 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.
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.