Unicity of Meromorphic Mappings

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 ℂ^m

   • 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

   PDF

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.

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

• 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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