Value Distribution of the *k*th Derivatives of Meromorphic Functions

Affiliation(s)

College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, China.

Department of Mathematics, University of Shanghai for Science and Technology, Shanghai, China.

College of Applied Mathematics, Chengdu University of Information Technology, Chengdu, China.

Department of Mathematics, University of Shanghai for Science and Technology, Shanghai, China.

ABSTRACT

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*k*th Derivatives of Meromorphic Functions," *Advances in Pure Mathematics*, Vol. 4 No. 1, 2014, pp. 11-16. doi: 10.4236/apm.2014.41002.

P. Yang and X. Liu, "Value Distribution of the

References

[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

[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