The maximum number of zeros of $r(z)-\overline{z}$ revisited

Abstract

Generalizing several previous results in the literature on rational harmonic functions, we derive bounds on the maximum number of zeros of functions $f(z)=\frac{p(z)}{q(z)}-\overline{z}$, which depend on both $\mathrm{deg}(p)$ and $\mathrm{deg}(q)$. Furthermore, we prove that any function that attains one of these upper bounds is regular.

Accepted for publication in CMFT

References in corpus (1)

• Perturbing rational harmonic functions by poles

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