Nevanlinna theory, normal families, and algebraic differential equations / Norbert Steinmetz.
Steinmetz, Norbert, 1949- author.
2017
QA331
Available Online

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Title Nevanlinna theory, normal families, and algebraic differential equations / Norbert Steinmetz.
Author Steinmetz, Norbert, 1949- author.
ISBN 9783319598000 (electronic book)
3319598007 (electronic book)
9783319597997
331959799X
DOI https://doi.org/10.1007/978-3-319-59800-0
Published Cham, Switzerland : Springer, 2017.
Language English
Description 1 online resource (xviii, 235 pages) : illustrations.
Item Number 10.1007/978-3-319-59800-0 doi
Call Number QA331
Dewey Decimal Classification 515/.9
Summary 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.-- Provided by publisher.
Note Includes index.
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed August 4, 2017).
Series Universitext.
Available in Other Form Print version: 331959799X
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Introduction and preface
Selected Topics in Complex Analysis
Nevanlinna Theory
Selected Applications of Nevanlinna Theory
Normal Families
Algebraic Differential Equations
Higher-Order Algebraic Differential Equations
Index.

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