Value Distribution of the kth Derivatives of Meromorphic Functions

In the paper, we take up a new method to prove a result of value distribution of meromorphic functions: let f be a meromorphic function in , and let , where P is a polynomial. Suppose that all zeros of f have multiplicity at least , except possibly finite many, and as . Then has infinitely many zeros.

Cite this paper

P. Yang and X. Liu, "Value Distribution of the kth Derivatives of Meromorphic Functions," Advances in Pure Mathematics, Vol. 4 No. 1, 2014, pp. 11-16. doi: 10.4236/apm.2014.41002.

Conflicts of Interest

The authors declare no conflicts of interest.

 [1] W. K. Hayman, “Picard Values of Meromorphic Functions and Their Derivatives,” Annals of Mathematics, Vol. 70, No. 1, 1959, pp. 9-42. http://dx.doi.org/10.2307/1969890 [2] X. J. Liu, S. Nevo and X. C. Pang, “On the kth Derivative of Meromorphic Functions with Zeros of Multiplicity at Least k+1,” Journal of Mathematical Analysis and Applications, Vol. 348, No. 1, 2008, pp. 516-529. http://dx.doi.org/10.1016/j.jmaa.2008.07.019 [3] S. Nevo, X. C. Pang and L. Zalcman, “Quasinormality and meromorphic functions with multiple zeros,” Journal d’Analyse Math??matique, Vol. 101, No. 1, 2007, pp. 1-23. [4] X. C. Pang, S. Nevo and L. Zalcman, “Derivatives of Meromorphic Functions with Multiple Zeros and Rational Functions,” Computational Methods and Function Theory, Vol. 8, No. 2, 2008, pp. 483-491. http://dx.doi.org/10.1007/BF03321700 [5] X. C. Pang and L. Zalcman, “Normal Families and Shared Values,” Bulletin London Mathematical Society, Vol. 32, No. 3, 2000, pp. 325-331. http://dx.doi.org/10.1112/S002460939900644X