Variation on a Theorem by Mues and Steinmetz

Abstract

Let $f$ be a meromorphic function. We suggest a generalization of $f$ and its derivative $f^{\prime }$ sharing a nonzero value $a$ IM that does not impose any a priori restrictions on the ramification of $f$. Then we discuss some results around the question whether the famous theorem on entire functions $f$ that share two values IM with $f^{\prime }$ still holds for this weaker notion.

11 pages

References in corpus (1)

• Entire functions sharing simple $a$-points with their first derivative