Angular value distribution concerning shared values (Q261666)

The authors investigate the value distribution of a meromorphic function in an angular region in connection to the value sharing with its derivative and prove the following result: Let \(f\) be a meromorphic function in \(\mathbb{C}\) with lower order greater than \(2\). Then there exists a direction \(H : \arg z = \theta_{0}\) (\(0 \leq \theta_{0} \leq 2\pi\)) such that for any positive number \(\varepsilon\), \(f\) and \(f'\) share at most two distinct finite values ignoring multiplicities in the angular region \(\{z : |\arg z - \theta_{0} | < \varepsilon\}\). The result improves an earlier result.