On unique range sets of meromorphic functions in $\mathbb{C}^m$
Bai, Xiao-Tian ; Han, Qi
Archivum Mathematicum, Tome 043 (2007), p. 185-195 / Harvested from Czech Digital Mathematics Library

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 $5\le c_3(\mathcal {M}(\mathbb {C}^m))\le 6$.

Publié le : 2007-01-01
Classification:  32A22
@article{108064,
     author = {Xiao-Tian Bai and Qi Han},
     title = {On unique range sets of meromorphic functions in $\mathbb{C}^m$},
     journal = {Archivum Mathematicum},
     volume = {043},
     year = {2007},
     pages = {185-195},
     zbl = {1164.32001},
     mrnumber = {2354807},
     language = {en},
     url = {http://dml.mathdoc.fr/item/108064}
}
Bai, Xiao-Tian; Han, Qi. On unique range sets of meromorphic functions in $\mathbb{C}^m$. Archivum Mathematicum, Tome 043 (2007) pp. 185-195. http://gdmltest.u-ga.fr/item/108064/

Bernstein C. A.; Chang D. C.; Li B. Q. Shared values for meromorphic functions, Adv. Math. 115 (1995), 201–220. (1995) | MR 1354669

Fang M. L. On the uniqueness of admissible meromorphic functions in the unit disc, Sci. China Ser. A 28 (1998), 1056–1074. (1998) | MR 1703235

Fujimoto H. The uniqueness problem of meromorphic maps into the complex projective space, Nagoya Math. J. 58 (1975), 1–23. (1975) | MR 0393586 | Zbl 0313.32005

Gackstatter F.; Laine I. Zur Theorie der gew$\ddot{o}$hnlichen Differentialgleichungen im Komplexen, Ann. Polon. Math. 38 (1980), 259–287. (1980) | MR 0599252

Gross F. On the distribution of values of meromorphic functionas, Trans. Amer. Math. Soc. 131 (1968), 199–214. (1968) | MR 0220938

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. (1976) | MR 0450529

Hayman W. K. Meromorphic Functions, Clarendon Press, Oxford, 1964. (1964) | MR 0164038 | Zbl 0115.06203

Hu P. C.; Li C.; Yang C. C. Unicity of Meromorphic Mappings, Kluwer Academic, Dordrecht, 2003. | MR 1988768 | Zbl 1074.30002

Jin L.; Ru M. A unicity theorem for moving targets counting multiplicities, Tôhoku Math. J. 57 (2005), 589–595. | MR 2203548 | Zbl 1106.32017

Vitter A. The lemma of the logarithmic derivative in several complex variables, Duke Math. J. 44 (1977), 89–104. (1977) | MR 0432924 | Zbl 0361.32003

Yang C. C.; Yi H. X. Uniqueness Theory of Meromorphic Functions, Science Press & Kluwer Academic, Beijing & Dordrecht, 2003. | MR 2105668 | Zbl 1070.30011

Yi H. X. On a question of Gross concerning uniqueness of entire functions, Bull. Austral. Math. Soc. 57 (1998), 343–349. (1998) | MR 1617332 | Zbl 0905.30026