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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
MathSciNet review:
2218629
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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:
-
- 1.
- 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)
- 2.
- H. H. Chen and M. L. Fang, On the value distribution of
 Sci. China Ser. A 38 (1995), 789-798. MR 1360682 (97a:30035) - 3.
- W. K. Hayman, Picard values of meromorphic functions and their derivatives, Ann. of Math. (2) 70 (1959), 9-42. MR 0110807 (22:1675)
- 4.
- 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)
- 5.
- X. C. Pang, Sh. Nevo, and L. Zalcman, Quasinormal families of meromorphic functions, Rev. Mat. Iberoamericana 21 (2005), 249-262. MR 2155021 (2006d:30046)
- 6.
- 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)
- 7.
- L. Zalcman, On some questions of Hayman, unpublished manuscript, 1994.
- 8.
- L. Zalcman, Normal families: new perspectives, Bull. Amer. Math. Soc. (N.S.) 35 (1998), 215-230. MR 1624862 (99g:30048)
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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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