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On the number of zeros of certain rational harmonic functions

Dmitry Khavinson·Genevra Neumann
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Abstract

Extending a result from the paper of D. Khavinson and G. Swiatek, we show that the rational harmonic function $\bar{r(z)} - z$, where r(z) is a rational function of degree n > 1, has no more than 5n - 5 complex zeros. Applications to gravitational lensing are discussed. In particular, this result settles a conjecture of S. H. Rhie concerning the maximum number of lensed images due to an n-point gravitational lens.

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Dmitry Khavinson, Genevra Neumann. 2004-03-05. On the number of zeros of certain rational harmonic functions. https://arxiv.org/abs/math/0401188

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