The Maximum Number of Zeros of r(z)-z¯ Revisited - Liesen, Jörg; Zur, Jan (Computational methods and function theory, 2018)
Generalizing several previous results in the literature on rational harmonic functions, we derive bounds on the maximum number of zeros of functions f ( z ) = p ( z ) q ( z ) - z ¯ , which depend on both deg ( p ) and deg ( q ) . Furthermore, we prove that any function that attains one of these upper bounds is regular.