Value Distribution Theory and Related Topics

  • G. Barsegian
  • I. Laine
  • C. C. Yang

Part of the Advances in Complex Analysis and Its Applications book series (ACAA, volume 3)

Table of contents

  1. Front Matter
    Pages i-vii
  2. Geometric value distribution theory

  3. Classical value distribution theory

    1. G. A. Barsegian, C. C. Yang
      Pages 105-116
    2. E. Ciechanowicz, I. I. Marchenko
      Pages 117-129
    3. Risto Korhonen
      Pages 167-179
    4. I. I. Marchenko, I. G. Nikolenko
      Pages 181-188
  4. Complex differential and functional equations

    1. G. A. Barsegian, A. A. Sarkisian, C. C. Yang
      Pages 189-199
    2. Ha Huy Khoai, Yang C. C.
      Pages 201-207
    3. Chung-Chun Yang, Ping Li
      Pages 219-231
  5. Several variables theory

About this book

Introduction

The Nevanlinna theory of value distribution of meromorphic functions, one of the milestones of complex analysis during the last century, was c- ated to extend the classical results concerning the distribution of of entire functions to the more general setting of meromorphic functions. Later on, a similar reasoning has been applied to algebroid functions, subharmonic functions and meromorphic functions on Riemann surfaces as well as to - alytic functions of several complex variables, holomorphic and meromorphic mappings and to the theory of minimal surfaces. Moreover, several appli- tions of the theory have been exploited, including complex differential and functional equations, complex dynamics and Diophantine equations. The main emphasis of this collection is to direct attention to a number of recently developed novel ideas and generalizations that relate to the - velopment of value distribution theory and its applications. In particular, we mean a recent theory that replaces the conventional consideration of counting within a disc by an analysis of their geometric locations. Another such example is presented by the generalizations of the second main theorem to higher dimensional cases by using the jet theory. Moreover, s- ilar ideas apparently may be applied to several related areas as well, such as to partial differential equations and to differential geometry. Indeed, most of these applications go back to the problem of analyzing zeros of certain complex or real functions, meaning in fact to investigate level sets or level surfaces.

Keywords

Complex analysis Meromorphic function Nevanlinna theory calculus differential equation functional equation maximum

Editors and affiliations

  • G. Barsegian
    • 1
  • I. Laine
    • 2
  • C. C. Yang
    • 3
  1. 1.National Academy of Sciences of ArmeniaYerevanArmenia
  2. 2.University of JoensuuJoensuuFinland
  3. 3.Hong Kong University of Science and TechnologyHong Kong, China

Bibliographic information

  • DOI https://doi.org/10.1007/b131070
  • Copyright Information Kluwer Academic Publishers 2004
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4020-7950-4
  • Online ISBN 978-1-4020-7951-1
  • About this book