Picard-Hayman behavior of derivatives of meromorphic functions with multiple zeros
Authors:
Shahar Nevo, Xuecheng Pang and Lawrence Zalcman
Journal:
Electron. Res. Announc. Amer. Math. Soc. 12 (2006), 37-43
MSC (2000):
Primary 30D35, 30D45
DOI:
https://doi.org/10.1090/S1079-6762-06-00158-2
Published electronically:
March 31, 2006
MathSciNet review:
2218629
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: The derivative of a transcendental meromorphic function all of whose zeros are multiple assumes every nonzero complex value infinitely often.
- Walter Bergweiler and Alexandre Eremenko, On the singularities of the inverse to a meromorphic function of finite order, Rev. Mat. Iberoamericana 11 (1995), no. 2, 355–373. MR 1344897, DOI https://doi.org/10.4171/RMI/176
- Huai Hui Chen and Ming Liang Fang, The value distribution of $f^nf’$, Sci. China Ser. A 38 (1995), no. 7, 789–798. MR 1360682
- W. K. Hayman, Picard values of meromorphic functions and their derivatives, Ann. of Math. (2) 70 (1959), 9–42. MR 110807, DOI https://doi.org/10.2307/1969890
- Yong Xing Ku, A criterion for normality of families of meromorphic functions, Sci. Sinica Special Issue I on Math. (1979), 267–274 (Chinese, with French summary). MR 662205
- Xuecheng Pang, Shahar Nevo, and Lawrence Zalcman, Quasinormal families of meromorphic functions, Rev. Mat. Iberoamericana 21 (2005), no. 1, 249–262. MR 2155021, DOI https://doi.org/10.4171/RMI/422
- Yuefei Wang and Mingliang Fang, Picard values and normal families of meromorphic functions with multiple zeros, Acta Math. Sinica (N.S.) 14 (1998), no. 1, 17–26. MR 1694044, DOI https://doi.org/10.1007/BF02563879
7 L. Zalcman, On some questions of Hayman, unpublished manuscript, 1994.
- Lawrence Zalcman, Normal families: new perspectives, Bull. Amer. Math. Soc. (N.S.) 35 (1998), no. 3, 215–230. MR 1624862, DOI https://doi.org/10.1090/S0273-0979-98-00755-1
5 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.
6 H. H. Chen and M. L. Fang, On the value distribution of $f^nf’,$ Sci. China Ser. A 38 (1995), 789–798.
1 W. K. Hayman, Picard values of meromorphic functions and their derivatives, Ann. of Math. (2) 70 (1959), 9–42.
2 Y. X. Ku, Un critère de normalité des familles de fonctions méromorphes, Sci. Sinica Special Issue 1 (1979), 267–274. (Chinese)
8 X. C. Pang, Sh. Nevo, and L. Zalcman, Quasinormal families of meromorphic functions, Rev. Mat. Iberoamericana 21 (2005), 249–262.
4 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.
7 L. Zalcman, On some questions of Hayman, unpublished manuscript, 1994.
3 L. Zalcman, Normal families: new perspectives, Bull. Amer. Math. Soc. (N.S.) 35 (1998), 215–230.
Similar Articles
Retrieve articles in Electronic Research Announcements of the American Mathematical Society
with MSC (2000):
30D35,
30D45
Retrieve articles in all journals
with MSC (2000):
30D35,
30D45
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
MR Author ID:
228232
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
Keywords:
Meromorphic functions,
quasinormal families.
Received by editor(s):
November 23, 2005
Published electronically:
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
Article copyright:
© Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
