Zeros and Uniqueness of Difference Polynomials of Meromorphic Functions
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This research is a continuation of a recent paper due to the first author in [9]. Different from previous results, we investigate the value distribution of difference polynomialsof moromorphic functions in this paper. In particular, we are interested in theexistence of zeros of f(z)n(λf(z +c)m +μf(z)m)-a, where f is a moromorphic function,n, m are two non-negative integers, and λ, μ are non-zero complex numbers. However, theproof here is obviously different to the one in [9]. We also study difference polynomials ofentire functions sharing a common value, which improves the result in [10, 13].
Abstract
This research is a continuation of a recent paper due to the first author in [9]. Different from previous results, we investigate the value distribution of difference polynomialsof moromorphic functions in this paper. In particular, we are interested in theexistence of zeros of f(z)n(λf(z +c)m +μf(z)m)-a, where f is a moromorphic function,n, m are two non-negative integers, and λ, μ are non-zero complex numbers. However, theproof here is obviously different to the one in [9]. We also study difference polynomials ofentire functions sharing a common value, which improves the result in [10, 13].
참고문헌 (13)
- W. Bergweiler, "On the singularities of the inverse to a meromorphic function of finite order", Rev. Mat. Iberoamericana, 11, pp.355~373 (1995)
- Y. M. Chiang, "On the Nevanlinna characteristic of f(z + ) and difference equations in the complex plane", Ramanujan J, 16(1), pp.105~129 (2008)
- R. G. Halburd, "Nevanlinna theory for the difference operator", Ann. Acad. Sci. Fenn., 31, pp.463~478 (2006)
- W. K. Hayman, "Picard values of meromorphic functions and their derivatives", Ann. of Math., 70, pp.9~42 (1959)
- J. Heittokangas, "Value sharing results for shifts of meromorphic function, and sufficient conditions for periodicity", J. Math. Anal. Appl., 355, pp.352~363 (2009)
- I. Laine, "Value Distribution of Difference Polynomials", Proc. Japan Acad. Ser. A Math. Sci., 83, pp.148~151 (2007)
- K. Liu, "Value distribution of the difference operator", Arch. Math, 92, pp.270~278 (2009)
- E. Mues, "¨U ber ein Problem von Hayman", Math. Z., 164, pp.239~259 (1979)
- X. G. Qi, "Uniqueness and value distribution of differences of entire functions", J. Math. Anal. Appl., 379(1), pp.180~187 (2011)
- X. G. Qi, "Value distribution and uniqueness of difference polynomials and entire solutions of difference equations", Ann. Polon. Math, 102, pp.129~142 (2011)
- Junfeng Xu, "Uniqueness of Entire Functions and Differential Polynomials", 대한수학회보, 44(4), pp.623~629 (2007), 대한수학회
- C. C. Yang, "Uniqueness Theory of Meromorphic Functions" (2003), Kluwer Academic Publishers
- J. L. Zhang, "Value distribution and shared sets of differences of meromorphic functions", J. Math. Anal. Appl., 367, pp.401~408 (2010)