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Unicity of Meromorphic Mappings

  • Pei-Chu Hu
  • Ping Li
  • Chung-Chun Yang

Part of the Advances in Complex Analysis and its Applications book series (ACAA, volume 1)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Pei-Chu Hu, Ping Li, Chung-Chun Yang
    Pages 1-117
  3. Pei-Chu Hu, Ping Li, Chung-Chun Yang
    Pages 119-210
  4. Pei-Chu Hu, Ping Li, Chung-Chun Yang
    Pages 211-307
  5. Pei-Chu Hu, Ping Li, Chung-Chun Yang
    Pages 309-378
  6. Pei-Chu Hu, Ping Li, Chung-Chun Yang
    Pages 379-439
  7. Back Matter
    Pages 441-467

About this book

Introduction

For a given meromorphic function I(z) and an arbitrary value a, Nevanlinna's value distribution theory, which can be derived from the well known Poisson-Jensen for­ mula, deals with relationships between the growth of the function and quantitative estimations of the roots of the equation: 1 (z) - a = O. In the 1920s as an application of the celebrated Nevanlinna's value distribution theory of meromorphic functions, R. Nevanlinna [188] himself proved that for two nonconstant meromorphic func­ tions I, 9 and five distinctive values ai (i = 1,2,3,4,5) in the extended plane, if 1 1- (ai) = g-l(ai) 1M (ignoring multiplicities) for i = 1,2,3,4,5, then 1 = g. Fur­ 1 thermore, if 1- (ai) = g-l(ai) CM (counting multiplicities) for i = 1,2,3 and 4, then 1 = L(g), where L denotes a suitable Mobius transformation. Then in the 19708, F. Gross and C. C. Yang started to study the similar but more general questions of two functions that share sets of values. For instance, they proved that if 1 and 9 are two nonconstant entire functions and 8 , 82 and 83 are three distinctive finite sets such 1 1 that 1- (8 ) = g-1(8 ) CM for i = 1,2,3, then 1 = g.

Keywords

Algebroid Derivative Heine–Borel theorem Meromorphic function Nevanlinna theory Wronskian logarithm manifold

Authors and affiliations

  • Pei-Chu Hu
    • 1
  • Ping Li
    • 2
  • Chung-Chun Yang
    • 3
  1. 1.Department of MathematicsShandong UniversityJinan, ShandongChina
  2. 2.Department of MathematicsUniversity of Science and Technology of ChinaHefei, AnhuiChina
  3. 3.Department of MathematicsThe Hong Kong University of Science and TechnologyHong KongChina

Bibliographic information