复差分多项式的亏量
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摘要
利用亚纯函数的Nevanlinna值分布理论,研究了差分多项式的亏量问题,得到了关于有限级亚纯函数差分多项式亏量的一些结果,其中部分结果可视为微分多项式相应结果的差分模拟,这些结果推广了前人已有的结论.
Using the Nevanlinna theory of the value distribution of meromorphic functions,the problem of deficiency of difference polynomial is studied.Some results on deficiencies of difference polynomials of meromorphic functions of finite order are given,some of which can be viewed as difference analogues of corresponding results of difference polynomials,these results improve previous findings.
Using the Nevanlinna theory of the value distribution of meromorphic functions,the problem of deficiency of difference polynomial is studied.Some results on deficiencies of difference polynomials of meromorphic functions of finite order are given,some of which can be viewed as difference analogues of corresponding results of difference polynomials,these results improve previous findings.
引文
[1]BHOOSNURMATH S S,KULKARNI M N,YU K W.On the value distribution of differential polynomials[J].Bull Korean Math Soc,2008,45(3):427-435.
[2]CLUNIE J.On a result of Hayman[J].J London Math Soc,1967,42:389-392.
[3]HAYKMAN W.Picard values of meromorphic functions and their derivatives[J].Ann Math,1959,71(1):9-42.
[4]MILLOUX H.Les fonctions meromorphes et leurs derives[M].Paris:Hermann,1940:20.
[5]YANG C C.On deficiecies of differential polynomials[J].Math Z,1970,116:197-204.
[6]郑秀敏,陈宗煊.某些差分多项式的亏量[J].数学学报,2011,54(6):983-992.
[7]HALBURD R G,KORHONEN R J.Difference analogue of the lemma on the logarithmic derivative with applications to difference equations[J].J Math Anal Appl,2006,314:477-487.
[8]HALBURD R G,KORHONEN R J.Finite-order meromorphic solutions and the discrete Painleve eqations[J].Proc London Math Soc,2007,94:443-474.
[9]HAYMAN W K.Meromorphic Functions[M].Oxford:Oxford University Press,1964:28-86.
[10]金瑾,李里.关于亚纯函数φ(z)f(z)M[f]的值分布[J].华中师范大学学报(自然科学版),2015,49(4):483-487.
[11]金瑾.关于亚纯函数φ(z)f(z)(f(k)(z))nP[f]的值分布[J].应用数学,2013,26(3):499-505.
[12]金瑾.关于高阶线性微分方程解与其小函数的增长性[J].上海交通大学学报(自然科学版),2013,47(7):1155-1159.
[13]金瑾.关于一类高阶齐次线性微分方程解的增长性[J].中山大学报(自然科学版),2013,52(1):51-55.
[14]金瑾.一类高阶齐次数性微分方程解的增长性[J].华中师范大学报(自然科学版),2013,47(1):4-7.
[15]金瑾,樊艺,左建军,等.一类亚纯系数高阶非齐次线性微分方程解与小函数的增长性[J].上海大学学报(自然科学版),2014,20(6):726-732.
[16]金瑾.单位圆内高阶齐次线性微分方程解与小函数的关系[J].应用数学学报,2014,37(4):254-264.
[17]金瑾.高阶差分方程组的亚纯解[J].应用数学,2015,28(2):292-298.
[18]金瑾,武玲玲,樊艺.高阶非线性微分方程组的亚纯允许解[J].东北师大学报(自然科学版),2015,47(1):22-25.
[19]金瑾.高阶非线性代数微分方程组的可允许解[J].安徽师范大学学报(自然科学版),2014,37(2):114-119.
[2]CLUNIE J.On a result of Hayman[J].J London Math Soc,1967,42:389-392.
[3]HAYKMAN W.Picard values of meromorphic functions and their derivatives[J].Ann Math,1959,71(1):9-42.
[4]MILLOUX H.Les fonctions meromorphes et leurs derives[M].Paris:Hermann,1940:20.
[5]YANG C C.On deficiecies of differential polynomials[J].Math Z,1970,116:197-204.
[6]郑秀敏,陈宗煊.某些差分多项式的亏量[J].数学学报,2011,54(6):983-992.
[7]HALBURD R G,KORHONEN R J.Difference analogue of the lemma on the logarithmic derivative with applications to difference equations[J].J Math Anal Appl,2006,314:477-487.
[8]HALBURD R G,KORHONEN R J.Finite-order meromorphic solutions and the discrete Painleve eqations[J].Proc London Math Soc,2007,94:443-474.
[9]HAYMAN W K.Meromorphic Functions[M].Oxford:Oxford University Press,1964:28-86.
[10]金瑾,李里.关于亚纯函数φ(z)f(z)M[f]的值分布[J].华中师范大学学报(自然科学版),2015,49(4):483-487.
[11]金瑾.关于亚纯函数φ(z)f(z)(f(k)(z))nP[f]的值分布[J].应用数学,2013,26(3):499-505.
[12]金瑾.关于高阶线性微分方程解与其小函数的增长性[J].上海交通大学学报(自然科学版),2013,47(7):1155-1159.
[13]金瑾.关于一类高阶齐次线性微分方程解的增长性[J].中山大学报(自然科学版),2013,52(1):51-55.
[14]金瑾.一类高阶齐次数性微分方程解的增长性[J].华中师范大学报(自然科学版),2013,47(1):4-7.
[15]金瑾,樊艺,左建军,等.一类亚纯系数高阶非齐次线性微分方程解与小函数的增长性[J].上海大学学报(自然科学版),2014,20(6):726-732.
[16]金瑾.单位圆内高阶齐次线性微分方程解与小函数的关系[J].应用数学学报,2014,37(4):254-264.
[17]金瑾.高阶差分方程组的亚纯解[J].应用数学,2015,28(2):292-298.
[18]金瑾,武玲玲,樊艺.高阶非线性微分方程组的亚纯允许解[J].东北师大学报(自然科学版),2015,47(1):22-25.
[19]金瑾.高阶非线性代数微分方程组的可允许解[J].安徽师范大学学报(自然科学版),2014,37(2):114-119.