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arXiv · 1403.0906

Perturbing rational harmonic functions by poles

Olivier Sète·Robert Luce·Jörg Liesen
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Abstract

We study how adding certain poles to rational harmonic functions of the form $R(z)-\bar{z}$, with $R(z)$ rational and of degree $d\geq 2$, affects the number of zeros of the resulting functions. Our results are motivated by and generalize a construction of Rhie derived in the context of gravitational microlensing (ArXiv e-print 2003). Of particular interest is the construction and the behavior of rational functions $R(z)$ that are {\em extremal} in the sense that $R(z)-\bar{z}$ has the maximal possible number of $5(d-1)$ zeros.

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Olivier Sète, Robert Luce, Jörg Liesen. 2014-03-04. Perturbing rational harmonic functions by poles. https://doi.org/10.1007/s40315-014-0083-x

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