﻿ 亚纯函数与微分多项式分担小函数的唯一性 Uniqueness of Meromorphic Function and Its Differential Polynomial Sharing Small Functions

Pure Mathematics
Vol.05 No.05(2015), Article ID:16065,7 pages
10.12677/PM.2015.55030

Uniqueness of Meromorphic Function and Its Differential Polynomial Sharing Small Functions

Chengwei Yang, Dan Liu

Institute of Applied Mathematics, South China Agricultural University, Guangzhou Guangdong

Received: Aug. 30th, 2015; accepted: Sep. 18th, 2015; published: Sep. 21st, 2015

ABSTRACT

In this paper, we study the uniqueness of meromorphic function and its differential polynomial sharing two small functions, and prove the follow theory. Let be a nonconstant meromorphic function satisfying, let be an integer and let and be two distinct small functions related to. Let, where are small functions related to. If and share and CM almost, then. Thus, this result improves some existing results.

Keywords:Meromorphic Function, Sharing Function, Differential Polynomial, Uniqueness

1. 引言与主要结果

1976年，Ruble L. A.和Yang C. C. [3] 证明了：若整函数及其一阶导数CM分担两个不同的有穷复数，则。自此以来，对于这一结果的改进和研究一直在继续。1983年，Gundersen G. G. [4] 证明了将整函数换为亚纯函数，上述结果仍然成立；1994年，顾永兴[5] 将一阶导数换为更为一般的的线性微分多项式，在满足的条件下，有成立，并猜测条件是可以去掉的；1995年，方明亮[6] 去掉了条件，证明了更一般的结果：对于满足的亚纯函数及其线性微分多项式，若几乎CM分担两个不同的有穷复数，则；2002年，王建平[7] 将方明亮结果中分担两个常数的情形推广到了分担两个小函数的情形；2006年，陈春芳[8] 在王建平结果的基础上，将这一限制推广为

2. 主要引理

3. 定理的证明

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Uniqueness of Meromorphic Function and Its Differential Polynomial Sharing Small Functions[J]. 理论数学, 2015, 05(05): 212-218. http://dx.doi.org/10.12677/PM.2015.55030

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