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Unicity of Meromorphic Mappings

  • Book
  • © 2003

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Authors:
  1. Pei-Chu Hu

    1. Department of Mathematics, Shandong University, Jinan, Shandong, China

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  2. Ping Li

    1. Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, China

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  3. Chung-Chun Yang

    1. Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong, China

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

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-ix
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  2. Nevanlinna theory

    • Pei-Chu Hu, Ping Li, Chung-Chun Yang
    Pages 1-117

  3. Uniqueness of meromorphic functions on ℂ

    • Pei-Chu Hu, Ping Li, Chung-Chun Yang
    Pages 119-210

  4. Uniqueness of meromorphic functions on ℂm

    • Pei-Chu Hu, Ping Li, Chung-Chun Yang
    Pages 211-307

  5. Uniqueness of meromorphic mappings

    • Pei-Chu Hu, Ping Li, Chung-Chun Yang
    Pages 309-378

  6. Algebroid functions of several variables

    • Pei-Chu Hu, Ping Li, Chung-Chun Yang
    Pages 379-439

  7. Back Matter

    Pages 441-467
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, Shandong University, Jinan, Shandong, China

    Pei-Chu Hu

  • Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, China

    Ping Li

  • Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong, China

    Chung-Chun Yang

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