On unique range sets of meromorphic functions in $\mathbb{C}^m$

Xiao-Tian Bai, Qi Ha

Address. School of Mathematics and System Sciences, Shandong University, Jinan 250100, Shandong, People's Republic of China

E-mail: x.t.bai@163.com

Abstract. 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 $5\leq c_3(\mathcal{M}(\mathbb{C}^m))\leq 9$ to $5\leq c_3(\mathcal{M}(\mathbb{C}^m))\leq 6$.

AMSclassification. Primary 32A22. Secondly 32A20.

Keywords. Entire (holomorphic) functions, meromorphic functions, unique range sets, linearly (in)dependent.