Articles

ON PROPERTIES OF DIFFERENCE POLYNOMIALS

  • CHEN Zong-Xuan ,
  • HUANG Zhi-Bo ,
  • ZHENG Xiu-Min
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  • School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

Received date: 2009-02-09

  Revised date: 2009-05-01

  Online published: 2011-03-20

Supported by

This project was supported by the National Natural Science Foundation of  China (10871076).

Abstract

We study the value distribution of difference polynomials of meromorphic functions, and extend classical theorems of Tumura-Clunie type to difference polynomials. We also consider the value distribution of f(z)f(z+c).

Cite this article

CHEN Zong-Xuan , HUANG Zhi-Bo , ZHENG Xiu-Min . ON PROPERTIES OF DIFFERENCE POLYNOMIALS[J]. Acta mathematica scientia, Series B, 2011 , 31(2) : 627 -633 . DOI: 10.1016/S0252-9602(11)60262-2

References


[1]  Hayman W K. Meromorphic Functions. Oxford: Clarendon Press, 1964


[2]  Laine I. Nevanlinna Theory and Complex Differential Equations. Berlin: W de Gruyter, 1993


[3]  Yang Lo. Value Distribution Theory and New Research. Beijing: Science Press, 1982 (in Chinese)


[4]  Clunie J. On integral and meromorphic functions. J London Math Soc, 1962, 37: 17--27


[5]  Mues E, Steinmetz N. The theorem of Tumura-Clunie for meromorphic functions. J London Math Soc, 1981, 23(2): 113--122


[6]  Ablowitz B, Halburd R G, Herbst B. On the extension of Painlev\'{e} property to difference equations. Nonlinearty, 2000, 13: 889--905


[7]  Bergweiler W, Langley J K. Zeros of differences of meromorphic functions. Math Proc Camb Phil Soc, 2007, 142: 133--147


[8]  Chen Z X, Shon K H. On zeros and fixed points of differencers of meromorphic functions. J Math Anal Appl, 2008, 344: 373--383


[9]  Chiang Y M, Feng S J. On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane. Ramanujan J, 2008,  16: 105--129.


[10]  Halburd R G, Korhonen R. Difference analogue of the lemma on the logarithmic derivative with applications to difference equations. J Math Anal Appl, 2006, 314: 477--487


[11]  Halburd R G, Korhonen R. Nevanlinna theory for the difference operator. Ann  Acad Sci Fenn Math, 2006, 31: 463--478


[12]  Heittokangas J, Korhonen R, Laine I, et al. Complex difference equations of Malmquist type. Comput Methods Funct Theory, 2001, 1: 27--39


[13]  Ishizaki K, Yanagihara N. Wiman-Valiron method for difference equations. Nagoya Math J, 2004, 175: 75--102


[14]  Laine I, Yang C C. Value distribution of difference polynomials. Proc Japan Acad, 2007, 83A: 148--151


[15]  Laine I,  Yang C C. Clunie theorems for difference and q-differene polynomials. J London Math Soc, 2007, 76(3): 556--566


[16]  Yi H X, Yang C C. The Uniqueness Theory of Meromorphic Functions. Beijing: Science Press, 1995 (in Chinese)


[17]  Chen Z X, Shon K H. Subnormal solutions of differential equaitons with periodic coefficients. Acta Mthematica Scientia, 2010, 30(1): 75--88

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