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

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Xiao-Tian Bai, Qi Ha
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** Address.**
School of Mathematics and System Sciences,
Shandong University, Jinan 250100, Shandong, People's
Republic of China

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

k.l.han@tom.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.