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Value Distribution Theory

  • Yang Lo

Table of contents

  1. Front Matter
    Pages i-xii
  2. Yang Lo
    Pages 1-41
  3. Yang Lo
    Pages 42-57
  4. Yang Lo
    Pages 58-92
  5. Yang Lo
    Pages 138-171
  6. Back Matter
    Pages 259-269

About this book

Introduction

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.

Keywords

Meromorphe Funktionen Meromorphic function Nevanlinna theory Value Distribution Werteverteilung derivative development distribution field form knowledge time

Authors and affiliations

  • Yang Lo
    • 1
  1. 1.Institute of MathematicsAcademia SinicaThe People’s Republic of China

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-02915-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-662-02917-6
  • Online ISBN 978-3-662-02915-2
  • Buy this book on publisher's site
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