# Article

Full entry | PDF   (0.2 MB)
Keywords:
entire (holomorphic) functions; meromorphic functions; unique range sets; linearly (in)dependent
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 $5\le c_3(\mathcal {M}(\mathbb {C}^m))\le 6$.
References:
[1] Bernstein C. A., Chang D. C., Li B. Q.: Shared values for meromorphic functions. Adv. Math. 115 (1995), 201–220. MR 1354669
[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
[3] Fujimoto H.: The uniqueness problem of meromorphic maps into the complex projective space. Nagoya Math. J. 58 (1975), 1–23. MR 0393586 | Zbl 0313.32005
[4] Gackstatter F., Laine I.: Zur Theorie der gew$\ddot{o}$hnlichen Differentialgleichungen im Komplexen. Ann. Polon. Math. 38 (1980), 259–287. MR 0599252
[5] Gross F.: On the distribution of values of meromorphic functionas. Trans. Amer. Math. Soc. 131 (1968), 199–214. MR 0220938
[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
[7] Hayman W. K.: Meromorphic Functions. Clarendon Press, Oxford, 1964. MR 0164038 | Zbl 0115.06203
[8] Hu P. C., Li C., Yang C. C.: Unicity of Meromorphic Mappings. Kluwer Academic, Dordrecht, 2003. MR 1988768 | Zbl 1074.30002
[9] Jin L., Ru M.: A unicity theorem for moving targets counting multiplicities. Tôhoku Math. J. 57 (2005), 589–595. MR 2203548 | Zbl 1106.32017
[10] Vitter A.: The lemma of the logarithmic derivative in several complex variables. Duke Math. J. 44 (1977), 89–104. MR 0432924 | Zbl 0361.32003
[11] Yang C. C., Yi H. X.: Uniqueness Theory of Meromorphic Functions. Science Press & Kluwer Academic, Beijing & Dordrecht, 2003. MR 2105668 | Zbl 1070.30011
[12] Yi H. X.: On a question of Gross concerning uniqueness of entire functions. Bull. Austral. Math. Soc. 57 (1998), 343–349. MR 1617332 | Zbl 0905.30026

Partner of