An entire function that shares a small function with a homogeneous differential polynomial (Q2014567)

Let \(f\) and \(g\) be two meromorphic functions in the open complex plane \(\mathbb C\). For \(a \in \mathbb C \cup \{\infty\}\), we say that \(f\) and \(g\) share the value \(a\) \(\mathcal{CM}\) (counting multiplicities) if and only if \(f-a\) and \(g-a\) have the same set of zeros with the same multiplicities, where by a zero of \(f-\infty\) we mean a pole of \(f\). In the paper the authors consider the problem of sharing a small function by an entire function and a homogeneous differential polynomial generated by the function.