具有兩個權(quán)分擔(dān)的公共值集的亞純函數(shù)

李進東,謝莉

(1.成都理工大學(xué)信息管理學(xué)院數(shù)學(xué)部,四川成都 610059; 2.西華師范大學(xué)數(shù)學(xué)與信息學(xué)院,四川南充 637002)

具有兩個權(quán)分擔(dān)的公共值集的亞純函數(shù)

李進東1,謝莉2

(1.成都理工大學(xué)信息管理學(xué)院數(shù)學(xué)部,四川成都 610059; 2.西華師范大學(xué)數(shù)學(xué)與信息學(xué)院,四川南充 637002)

討論了亞純函數(shù)分擔(dān)兩個集合的唯一性問題,證明了一個定理.所得結(jié)果改進了先前的一些定理,例子表明結(jié)果是精確的.

亞純函數(shù)；公共值集；唯一性

1 引言和主要結(jié)果

2 主要引理

3 定理1的證明

由此,引理2的結(jié)論(i)不成立.而根據(jù)引理4的結(jié)論,引理2的結(jié)論(iii)也不成立.所以,我們得到引理2的結(jié)論(ii).再根據(jù)引理3,我們得到f≡g.

[1]儀洪勛,楊重駿.亞純函數(shù)的唯一性理論[M].北京:科學(xué)出版社,1995.

[2]G ross F.Factorization ofm erom orphic functions and some open prob lem s[M]//Com p lex Analysis,Lecture Notes in Math.,599(proc.con.univ.Kentucky,lexington,Kentucky 1976).Berlin:Springer-velag,1977.

[3]Y i Hongxun.A question of G ross and the uniqueness of entire functions[J].Nagoya Mathem atical Journal, 1995,138:343-349.

[4]儀洪勛.亞純函數(shù)的唯一性和G ross的一個問題[J].中國科學(xué):A輯,1994,24(5):457-466.

[5]Li Ping,Yang Chongjun.some further results on the uniqueness range sets of m erom orphic functions[J]. KodaiMathematical Journal,1995,18:437-450.

[6]Fang mingliang,Guo Hui.On m erom orphic functions sharing two values[J].Analysis,1997,17:355-366.

[7]Fang mingliang,Lahiri I.Unique range set for certain meromorphic functions[J].Indian Journal of Mathem atics,2003,45:141-150.

[8]Yi Hongxun.Uniqueness of meromorphic functions and question of G ross[J].Kyungpook Mathematical Journal,2006,46:437-444.

[9]Lahiri I,Banerjee A.Uniqueness ofmeromorphic functionswith deficient poles[J].Kyungpook Mathematical Journal,2004,44:575-584.

On the uniqueness ofm erom orphic functions that share Two sets by Weight

LIJin-dong1,XIE Li2

(1.Departm ent of Mathem atics,Chengdu University of Technology,Chengdu 610059,China; 2.College of Mathematics and Information,China West Normal University,Nanchong 637002,China)

This paper deals with the uniqueness of meromorphic functions sharing two sets and obtains a theorem that is im provem ents of form er results.M oreover,the exam p le show s that the result is sharp.

meromorphic functions,shared set,uniqueness

O174.52

A

1008-5513(2009)02-0372-05

2007-06-20.

四川省教育廳自然科學(xué)基金(2004A-108),成都理工大學(xué)科研項目(R 230249).

李進東(1975-),碩士,研究方向：復(fù)分析.

2000M SC:30D 35