Rocky Mountain Journal of Mathematics

Value distribution of differences of meromorphic functions

Kai Liu

Full-text: Open access

Article information

Rocky Mountain J. Math., Volume 41, Number 5 (2011), 1567-1584.

First available in Project Euclid: 26 September 2011

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 30D35: Distribution of values, Nevanlinna theory 39A05: General theory

Meromorphic functions difference products finite order exponent of convergence


Liu, Kai. Value distribution of differences of meromorphic functions. Rocky Mountain J. Math. 41 (2011), no. 5, 1567--1584. doi:10.1216/RMJ-2011-41-5-1567.

Export citation


  • W. Bergweiler and A. Eremenko, On the singularities of the inverse to a meromorphic function of finite order, Rev. Matem. Ibero. 11 (1995), 355-373.
  • W. Bergweiler and J.K. Langley, Zeros of difference of meromorphic functions, Math. Proc. Camb. Phil. Soc. 142 (2007), 133-147.
  • Z.X. Chen and K.H. Shon, On zeros and fixed points of difference of meromorphic functions, J. Math. Anal. Appl. 344 (2008), 373-383.
  • Y.M. Chiang and S.J. Feng, On the Nevanlinna characteristic $f(z+\eta)$ and difference equations in the complex plane, The Ramanujan J. 16 (2008), 105-129.
  • J. Clunie, On integral and meromorphic functions, J. London Math. Soc. 37 (1962), 17-27.
  • A. Eremenko, J.K. Langley and J. Rossi, On the zeros of meromorphic functions of the form $\sum_{k=1}^{\infty}\frac{a_{k}}{z-z_{k}}$, J. d'Analyse Math. 62 (1994), 271-286.
  • R.G. Halburd and R.J. Korhonen, Difference analogue of lemma on the logarithmic derivative with applications to difference equations, J. Math. Anal. Appl. 314 (2006), 477-487.
  • –––, Nevanlinna theory for the difference operator, Ann. Acad. Sci. Fenn. Math. 31 (2006), 463-478.
  • W.K. Hayman, Picard values of meromorphic functions and their derivatives, Ann. Math. 70 (1959), 9-42.
  • –––, Research problems in function theory, The Athlone Press, London, 1967.
  • –––, Meromorphic functions, Clarendon Press, Oxford, 1964.
  • –––, Slowly growing integral and subharmonic functions, Comment. Math. Helv. 34 (1960), 75-84.
  • I. Laine, Nevanlinna theory and complex differential equation, Walter de Gruyter, Berlin, 1993.
  • I. Laine and C.C. Yang, Value distribution of difference polynomials, Proc. Japan Acad. 83 (2007), 148-151.
  • –––, Clunie theorem for difference and $q$ difference polynomials, J. Lond. Math. Soc. 76 (2007), 556-566.
  • J. K. Langley, Value distribution of differences of meromorphic functions, Rocky Mountain J. Math. 41 (2011), 275-292.
  • E. Mues, Über ein Problem von Hayman, Math. Z. 164 (1979), 239-259.
  • C.C. Yang and H.X. Yi, Uniqueness theory of meromorphic functions, in Mathematics and its application, Kluwer Academic Publishers, Dordrecht, 2003.