Overview
- Authors:
-
-
Pei-Chu Hu
-
Department of Mathematics, Shandong University, Jinan, Shandong, China
-
Ping Li
-
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, China
-
Chung-Chun Yang
-
Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong, China
Access this book
Other ways to access
Table of contents (5 chapters)
-
-
- Pei-Chu Hu, Ping Li, Chung-Chun Yang
Pages 1-117
-
- Pei-Chu Hu, Ping Li, Chung-Chun Yang
Pages 119-210
-
- Pei-Chu Hu, Ping Li, Chung-Chun Yang
Pages 211-307
-
- Pei-Chu Hu, Ping Li, Chung-Chun Yang
Pages 309-378
-
- Pei-Chu Hu, Ping Li, Chung-Chun Yang
Pages 379-439
-
Back Matter
Pages 441-467
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