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Value Distribution Theory

  • Book
  • © 1993

Overview

Authors:
  1. Yang Lo

    1. Institute of Mathematics, Academia Sinica, The People’s Republic of China

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xii
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  2. Essentials of Nevanlinna Theory

    • Yang Lo
    Pages 1-41

  3. Normal Families

    • Yang Lo
    Pages 42-57

  4. Borel Directions

    • Yang Lo
    Pages 58-92

  5. Value Distribution of Meromorphic Functions Together with Their Derivatives

    • Yang Lo
    Pages 93-137

  6. Recent Studies on Borel Directions

    • Yang Lo
    Pages 138-171

  7. Deficient Values and Borel Directions of Meromorphic Functions

    • Yang Lo
    Pages 172-215

  8. The Spread Relation and Its Applications

    • Yang Lo
    Pages 216-258

  9. Back Matter

    Pages 259-269
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Keywords

About this book

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 < (0) satisfies -1' logn(r, J = a) \ 1m = 1\ r->oo logr for every finite complex value a, with at most one exception. This result, generally known as the Picard-Borel theorem, lay the foundation for the theory of value distribution and since then has been the source of many research papers on this subject.

Authors and Affiliations

  • Institute of Mathematics, Academia Sinica, The People’s Republic of China

    Yang Lo

Bibliographic Information

  • Book Title: Value Distribution Theory

  • Authors: Yang Lo

  • DOI: https://doi.org/10.1007/978-3-662-02915-2

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1993

  • Softcover ISBN: 978-3-662-02917-6Published: 03 October 2013

  • eBook ISBN: 978-3-662-02915-2Published: 17 April 2013

  • Edition Number: 1

  • Number of Pages: XII, 269

  • Number of Illustrations: 2 b/w illustrations

  • Additional Information: Jointly published with Science Press, Beijing. Original Chinese edition published by Science Press, Beijing 1982

  • Topics: Analysis

  • Industry Sectors: Energy, Utilities & Environment, Engineering, IT & Software

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