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Picard-Hayman behavior of derivatives of meromorphic functions with multiple zeros

Author(s): Shahar Nevo; Xuecheng Pang; Lawrence Zalcman
Journal: Electron. Res. Announc. Amer. Math. Soc. 12 (2006), 37-43.
MSC (2000): Primary 30D35, 30D45
Posted: March 31, 2006
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Abstract: The derivative of a transcendental meromorphic function all of whose zeros are multiple assumes every nonzero complex value infinitely often.

References:

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W. Bergweiler and A. Eremenko, On the singularities of the inverse to a meromorphic function of finite order, Rev. Mat. Iberoamericana 11 (1995), 355-373. MR 1344897 (96h:30055)

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H. H. Chen and M. L. Fang, On the value distribution of $ f^nf',$ Sci. China Ser. A 38 (1995), 789-798. MR 1360682 (97a:30035)

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W. K. Hayman, Picard values of meromorphic functions and their derivatives, Ann. of Math. (2) 70 (1959), 9-42. MR 0110807 (22:1675)

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Y. X. Ku, Un critère de normalité des familles de fonctions méromorphes, Sci. Sinica Special Issue 1 (1979), 267-274. (Chinese) MR 0662205 (83i:30047)

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X. C. Pang, Sh. Nevo, and L. Zalcman, Quasinormal families of meromorphic functions, Rev. Mat. Iberoamericana 21 (2005), 249-262. MR 2155021 (2006d:30046)

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Y. F. Wang and M. L. Fang, Picard values and normal families of meromorphic functions with multiple zeros, Acta Math. Sinica (N.S.) 14 (1998), 17-26. MR 1694044 (2000g:30026)

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Additional Information:

Shahar Nevo
Affiliation: Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel
Email: nevosh@macs.biu.ac.il

Xuecheng Pang
Affiliation: Department of Mathematics, East China Normal University, Shanghai 20062, P. R. China
Email: xcpang@euler.math.ecnu.edu.cn

Lawrence Zalcman
Affiliation: Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel
Email: zalcman@macs.biu.ac.il

DOI: 10.1090/S1079-6762-06-00158-2
PII: S 1079-6762(06)00158-2
Keywords: Meromorphic functions, quasinormal families.
Received by editor(s): November 23, 2005.
Posted: March 31, 2006
Additional Notes: This work was supported by the German-Israel Foundation for Scientific Research and Development G.I.F. Grant No. I-809-234-6/2003.
Communicated by: Svetlana Katok
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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