Meromorphic functions that share four values
Meromorphic functions that share four values
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DOI：
10.1090/s0002-9947-1983-0694375-0
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发表时间：
1983-02
影响因子：
1.3
通讯作者：
G. Gundersen
中科院分区：
文献类型：
--
作者：
G. Gundersen
R. Nevanlinna指出，如果两个不同的非常数亚纯函数共享四个重数值，则这两个函数是彼此的Mbbius变换，其中两个共享值是两个函数的Picard值，并且共享值的特定排列的交比等于-1。本文证明了：如果两个非常数亚纯函数分担两个重数计数值，并且分担两个忽略重数的值，则这两个函数分担全部四个重数计数值.
An old theorem of R. Nevanlinna states that if two distinct nonconstant meromorphic functions share four values counting multiplicities, then the functions are Mbbius transformations of each other, two of the shared values are Picard values for both functions, and the cross ratio of a particular permutation of the shared values equals -1. In this paper we show that if two nonconstant meromorphic functions share two values counting multiplicities and share two other values ignoring multiplicities, then the functions share all four values counting multiplicities.