复微分-差分多项式的零点
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摘要
主要研究了几个不同类型的微分差微分分多项式的零点情况,利用文献[10]中公共零点、公共极点的思想,改善了原来定理的条件,得到了关于亚纯函数差分多项式的一些最新结果。
In this paper,we studied the zeros of complex differential-difference polynomials with different types.Using the idea of common zeros and common poles in the literature[10] we improved the conditions of the original theorems,and obtained some latest results about the differential-difference polynomials of meromorphic functions.
In this paper,we studied the zeros of complex differential-difference polynomials with different types.Using the idea of common zeros and common poles in the literature[10] we improved the conditions of the original theorems,and obtained some latest results about the differential-difference polynomials of meromorphic functions.
引文
[1] HAYMAN W K.Meromorphic functions[M]//Oxford Mathematical Monographs,Oxford:Clarendon Press,1964.
[2] LAINE I.Nevanlinna Theory and complex differential equations[M].Berlin:Walter de Gruyter,1993.
[3] YANG C C,YI H X.Uniqueness theory of meromorphic functions[M].Dordrecht:KluwerAcad Publ,2003.
[4] HAYMAN W K.Picard values of meromorphic functions and their derivatives[J].Ann Math,1959,70 9-42.
[5] MUES E.über ein Problem von Hayman(German)[J].Math Z,1979(164) 3:239-259.
[6] BERGWEILER W,EREMENKO A.On the singularities of the inverse to a mero orphic function of finite order[J].Rev Mat Iberoamericana,1995(11) 2:355-373.
[7] LAINE I,Yang C C.Value distribution of difference polynomials[J].Proc Jpn Acad Ser A Math Sci,2007,83,148-151 .
[8] LIU K,LIU X L,CAO T B.Uniqueness and zeros of q-shift difference polynomials[J].Proc Indian Acad Sci(Math Sci),2011(121)3:301-310.
[9] LIU K,Liu X L,Cao T B.Some difference results on Hayman conjecture and uniqueness[J].Bull of the Iran Math Soc,2011(38)4:1007-1020.
[10] 王琼燕,叶亚盛.亚纯函数差分多项式的值分布和唯一性[J].数学年刊,2014,A(卷),1-10.
[11] CHIANG Y M,FENG S J.On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane[J].Ramanujan J,2008(16) 1:105-129.
[12] HALBURD R G,KORHONEN R J.Meromorphic solutions of difference equations,integrability and the diacrete painlevé equations[J].J.Phys A,2007,320:1-38.
[2] LAINE I.Nevanlinna Theory and complex differential equations[M].Berlin:Walter de Gruyter,1993.
[3] YANG C C,YI H X.Uniqueness theory of meromorphic functions[M].Dordrecht:KluwerAcad Publ,2003.
[4] HAYMAN W K.Picard values of meromorphic functions and their derivatives[J].Ann Math,1959,70 9-42.
[5] MUES E.über ein Problem von Hayman(German)[J].Math Z,1979(164) 3:239-259.
[6] BERGWEILER W,EREMENKO A.On the singularities of the inverse to a mero orphic function of finite order[J].Rev Mat Iberoamericana,1995(11) 2:355-373.
[7] LAINE I,Yang C C.Value distribution of difference polynomials[J].Proc Jpn Acad Ser A Math Sci,2007,83,148-151 .
[8] LIU K,LIU X L,CAO T B.Uniqueness and zeros of q-shift difference polynomials[J].Proc Indian Acad Sci(Math Sci),2011(121)3:301-310.
[9] LIU K,Liu X L,Cao T B.Some difference results on Hayman conjecture and uniqueness[J].Bull of the Iran Math Soc,2011(38)4:1007-1020.
[10] 王琼燕,叶亚盛.亚纯函数差分多项式的值分布和唯一性[J].数学年刊,2014,A(卷),1-10.
[11] CHIANG Y M,FENG S J.On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane[J].Ramanujan J,2008(16) 1:105-129.
[12] HALBURD R G,KORHONEN R J.Meromorphic solutions of difference equations,integrability and the diacrete painlevé equations[J].J.Phys A,2007,320:1-38.