| 书目名称 | Unicity of Meromorphic Mappings | | 编辑 | Pei-Chu Hu,Ping Li,Chung-Chun Yang | | 视频video | | | 丛书名称 | Advances in Complex Analysis and Its Applications | | 图书封面 |  | | 描述 | 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. | | 出版日期 | Book 2003 | | 关键词 | Algebroid; Derivative; Heine–Borel theorem; Meromorphic function; Nevanlinna theory; Wronskian; logarithm; | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4757-3775-2 | | isbn_softcover | 978-1-4419-5243-1 | | isbn_ebook | 978-1-4757-3775-2 | | copyright | Springer-Verlag US 2003 |
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发表于 2025-3-21 16:21:11
