The maximum number of zeros of $r(z) - \overline{z}$ revisited
Jörg Liesen,
Jan Zur
Abstract: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.
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