On zeros and deficiencies of differences of meromorphic functions

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• 作者：Jianren Long (13) (14)
  Pengcheng Wu (14)
  Jun Zhu (15)
  
  13. School of Mathematical Sciences ; Xiamen University ; Xiamen ; 361005 ; P.R. China
  14. School of Mathematics and Computer Science ; Guizhou Normal University ; Guiyang ; 550001 ; P.R. China
  15. School of Mathematics Science ; Peking University ; Beijing ; 100871 ; P.R. China
  
• 关键词：complex difference ; zero ; deficiency
• 刊名：Advances in Difference Equations
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：2014
• 期：1
• 全文大小：183 KB
• 参考文献：1. Hayman, WK (1964) Meromorphic Functions. Clarendon, Oxford
  2. Laine, I (1993) Nevanlinna Theory and Complex Differential Equations. de Gruyter, Berlin CrossRef
  3. Yang, L (1993) Value Distribution Theory. Springer, Berlin
  4. Ablowitz, M, Halburd, RG, Herbst, B (2000) On the extension of Painlev茅 property to difference equations. Nonlinearity 13: pp. 889-905 CrossRef
  5. Bergweiler, W, Langley, JK (2007) Zeros of differences of meromorphic functions. Math. Proc. Camb. Philos. Soc 142: pp. 133-147 CrossRef
  6. Chiang, YM, Feng, SJ (2008) On the Nevanlinna characteristic of and difference equations in the complex plane. Ramanujan J 16: pp. 105-129 CrossRef
  7. Chen, ZX, Shon, KH (2009) Estimates for the zeros of differences of meromorphic functions. Sci. China Ser. A 52: pp. 2447-2458 CrossRef
  8. Halburd, RG, Korhonen, R (2006) Nevanlinna theory for the difference operator. Ann. Acad. Sci. Fenn., Math 31: pp. 463-478
  9. Halburd, RG, Korhonen, R (2006) Difference analogue of the lemma on the logarithmic derivative with applications to difference equations. J. Math. Anal. Appl 314: pp. 477-487 CrossRef
  10. Ishizaki, K, Yanagihara, N (2004) Wiman-Valiron method for difference equations. Nagoya Math. J 175: pp. 75-102
  11. Bergweiler, W, Eremenko, A, Rossi, J (1995) On the singularity of the inverse to a meromorphic function of finite order. Rev. Mat. Iberoam 11: pp. 355-373 CrossRef
  12. Eremenko, A, Langley, JK, Rossi, J (1994) On the zeros of meromorphic functions of the form. J. Anal. Math 62: pp. 271-286 CrossRef
  13. Hinchliffe, JD (2003) The Bergweiler-Eremenko theorem for finite lower order. Results Math 43: pp. 121-128 CrossRef
  14. Clunie, J, Eremenko, A, Rossi, J (1993) On equilibrium points of logarithmic and Newtonian potentials. J. Lond. Math. Soc 47: pp. 309-320 CrossRef
  15. Langley, JK (2011) Value distribution of differences of meromorphic functions. Rocky Mt. J. Math 41: pp. 275-291 CrossRef
  16. Boas, RP (1954) Entire Functions. Academic Press, New York
  17. Hayman, WK (1960) Slowly growing integral and subharmonic functions. Comment. Math. Helv 34: pp. 75-84 CrossRef
  18. Zhang, GH (1986) Theory of Entire and Meromorphic Functions-Deficient and Asymptotic Values and Singular Directions. Science Press, Beijing
  19. Barry, PD (1970) Some theorems related to the theorem. Proc. Lond. Math. Soc 21: pp. 334-360 CrossRef
  20. Laine, I, Wu, PC (2000) Growth of solutions of second order linear differential equations. Proc. Am. Math. Soc 128: pp. 2693-2703 CrossRef
  21. Hayman, WK (1974) The local growth of power series: a survey of the Wiman-Valiron method. Can. Math. Bull 17: pp. 317-358 CrossRef
  22. Hayman, WK (1989) Subharmonic Functions 螤. Academic Press, London
  
• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847

文摘

For a transcendental entire function in the complex plane, we study its divided differences . We partially prove a conjecture posed by Bergweiler and Langley under the additional condition that the lower order of is smaller than . Furthermore, we prove that if zero is a deficient value of , then , where . MSC: 30D35.