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Generalizing several previous results in the literature on rational harmonic functions, we derive bounds on the maximum number of zeros of functions $$f(z) = \frac{p(z)}{q(z)} - \overline{z}$$f(z)=p(z)q(z)-z¯, which depend on… Click to show full abstract
Generalizing several previous results in the literature on rational harmonic functions, we derive bounds on the maximum number of zeros of functions $$f(z) = \frac{p(z)}{q(z)} - \overline{z}$$f(z)=p(z)q(z)-z¯, which depend on both $$\mathrm{deg}(p)$$deg(p) and $$\mathrm{deg}(q)$$deg(q). Furthermore, we prove that any function that attains one of these upper bounds is regular.
Keywords:
maximum number;
deg;
zeros overline;
overline revisited;
number zeros
Journal Title: Computational Methods and Function Theory
Year Published: 2017
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Journal Title: Computational Methods and Function Theory
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!