Uniqueness theorems for meromorphic functions. II (Q2713054)

Let \(f(z)\) be a meromorphic function in the complex plane \(\mathbb{C}\) and \(k\) be a positive integer. For \(a\in\overline\mathbb{C}\), we denote by \(E_k' (a,f)\) the set of the roots of \(f(z)-a\) with multiplicity \(\leq k\), each root according to its multiplicity. Let \(S\) be a set of complex numbers and \(E_k(s,f)= \cup_{a\in S}E_k'(a,f)\). In this paper, the author proves that there exists a set with 7 elements such that any two entire functions satisfying \(E_2'(s,f)= E_2'(s,g)\) must be identical and there exists a set with 11 elements such that any two meromorphic functions satisfying \(E_2,(s,f)= E_3,(s,g)\) must be identical.