Abstract
Let f be a transcendental meromorphic function on ℂ, all but finitely many of whose zeros are multiple, and let R be a rational function, R ≢ 0. Then f′ − R has infinitely many zeros.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
W. Bergweiler and X. C. Pang, On the derivative of meromorphic functions with multiple zeros, J. Math. Anal. Appl. 278 (2003), 285–292.
C. T. Chuang, Normal Families of Meromorphic Functions, World Scientific, 1993.
W. K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, 1964.
O. Lehto and K. I. Virtanen, On the behaviour of meromorphic functions in the neighbourhood of an isolated singularity, Ann. Acad. Sci. Fenn. Ser. A 240 (1957), 1–23.
S. Nevo, X. C. Pang and L. Zalcman, Picard-Hayman behavior of derivatives of meromorphic functions with multiple zeros, Electron. Res. Announc. Amer. Math. Soc. 12 (2006), 37–43.
S. Nevo, X. C. Pang and L. Zalcman, Quasinormality and meromorphic functions with multiple zeros, J. Anal. Math. 101 (2007), 1–23.
Author information
Authors and Affiliations
Corresponding author
Additional information
Research supported by the German-Israeli Foundation for Scientific Research and Development, G.I.F. Grant No. G-809-234-6/2003, and by NNSF of China, Grant No. 10671067.
Rights and permissions
About this article
Cite this article
Pang, X., Nevo, S. & Zalcman, L. Derivatives of Meromorphic Functions with Multiple Zeros and Rational Functions. Comput. Methods Funct. Theory 8, 483–491 (2008). https://doi.org/10.1007/BF03321700
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03321700