| Title:
|
On unique range sets of meromorphic functions in $\mathbb{C}^m$ (English) |
| Author:
|
Bai, Xiao-Tian |
| Author:
|
Han, Qi |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
43 |
| Issue:
|
3 |
| Year:
|
2007 |
| Pages:
|
185-195 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
By considering a question proposed by F. Gross concerning unique range sets of entire functions in $\mathbb {C}$, we study the unicity of meromorphic functions in $\mathbb {C}^m$ that share three distinct finite sets CM and obtain some results which reduce $5\le c_3(\mathcal {M}(\mathbb {C}^m))\le 9$ to $5\le c_3(\mathcal {M}(\mathbb {C}^m))\le 6$. (English) |
| Keyword:
|
entire (holomorphic) functions |
| Keyword:
|
meromorphic functions |
| Keyword:
|
unique range sets |
| Keyword:
|
linearly (in)dependent |
| MSC:
|
32A22 |
| idZBL:
|
Zbl 1164.32001 |
| idMR:
|
MR2354807 |
| . |
| Date available:
|
2008-06-06T22:51:17Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108064 |
| . |
| Reference:
|
[1] Bernstein C. A., Chang D. C., Li B. Q.: Shared values for meromorphic functions.Adv. Math. 115 (1995), 201–220. MR 1354669 |
| Reference:
|
[2] Fang M. L.: On the uniqueness of admissible meromorphic functions in the unit disc.Sci. China Ser. A 28 (1998), 1056–1074. MR 1703235 |
| Reference:
|
[3] Fujimoto H.: The uniqueness problem of meromorphic maps into the complex projective space.Nagoya Math. J. 58 (1975), 1–23. Zbl 0313.32005, MR 0393586 |
| Reference:
|
[4] Gackstatter F., Laine I.: Zur Theorie der gew$\ddot{o}$hnlichen Differentialgleichungen im Komplexen.Ann. Polon. Math. 38 (1980), 259–287. MR 0599252 |
| Reference:
|
[5] Gross F.: On the distribution of values of meromorphic functionas.Trans. Amer. Math. Soc. 131 (1968), 199–214. MR 0220938 |
| Reference:
|
[6] Gross F.: Factorization of meromorphic functions and some open problems.Complex Analysis (Proc. Conf. Univ. Kentucky, Lexington, Kentucky, 1976), Lecture Notes in Math. 599, Springer, Berlin, 1977. MR 0450529 |
| Reference:
|
[7] Hayman W. K.: Meromorphic Functions.Clarendon Press, Oxford, 1964. Zbl 0115.06203, MR 0164038 |
| Reference:
|
[8] Hu P. C., Li C., Yang C. C.: Unicity of Meromorphic Mappings.Kluwer Academic, Dordrecht, 2003. Zbl 1074.30002, MR 1988768 |
| Reference:
|
[9] Jin L., Ru M.: A unicity theorem for moving targets counting multiplicities.Tôhoku Math. J. 57 (2005), 589–595. Zbl 1106.32017, MR 2203548 |
| Reference:
|
[10] Vitter A.: The lemma of the logarithmic derivative in several complex variables.Duke Math. J. 44 (1977), 89–104. Zbl 0361.32003, MR 0432924 |
| Reference:
|
[11] Yang C. C., Yi H. X.: Uniqueness Theory of Meromorphic Functions.Science Press & Kluwer Academic, Beijing & Dordrecht, 2003. Zbl 1070.30011, MR 2105668 |
| Reference:
|
[12] Yi H. X.: On a question of Gross concerning uniqueness of entire functions.Bull. Austral. Math. Soc. 57 (1998), 343–349. Zbl 0905.30026, MR 1617332 |
| . |
