Meromorphic functions that share a set with their derivatives (Q2473955)

Let \(h\) be meromorphic and \(S\) a set in the complex plane. Define \(E(S, h)=\bigcup_{a\in S}\{z\in\mathbb{C}: h(z)- a= 0\}\), where multiplicity is counted. The authors prove that there exists a set \(S\) having three elements such that if \(f\) is meromorphic, has at most finitely many simple poles and \(E(S, f)= E(S, f')\), then \(f\equiv f'\). Further, for some given sets \(S\), the authors explicitly list all possible meromorphic functions.