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On the number of zeros of certain rational harmonic functions |
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| Authors: | Dmitry Khavinson Genevra Neumann |
| Affiliation: | Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701 ; Department of Mathematics, Kansas State University, Manhattan, Kansas 66506 |
| Abstract: | Extending a result of Khavinson and Swiatek (2003) we show that the rational harmonic function  , where  is a rational function of degree  , has no more than  complex zeros. Applications to gravitational lensing are discussed. In particular, this result settles a conjecture by Rhie concerning the maximum number of lensed images due to an  -point gravitational lens. |
| Keywords: | Rational harmonic mappings fixed points argument principle gravitational lenses |
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