Derivatives of meromorphic functions with multiple zeros and small functions (Q1723828)

Summary: Let \(f \left(z\right)\) be a meromorphic function in \(\mathbb C\), and let \(\alpha \left(z\right) = R \left(z\right) h \left(z\right) \not\equiv 0\), where \(h \left(z\right)\) is a nonconstant elliptic function and \(R \left(z\right)\) is a rational function. Suppose that all zeros of \(f \left(z\right)\) are multiple except finitely many and \(T \left(r, \alpha\right) = o \left\{T \left(r, f\right)\right\}\) as \(r \rightarrow \infty\). Then \(f' \left(z\right) = \alpha \left(z\right)\) has infinitely many solutions.