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On the number of zeros of certain rational harmonic functions | Dmitry Khavinson
; Genevra Neumann
; | Date: |
15 Dec 2003 | Subject: | Complex Variables MSC-class: 26C15 (Primary); 30D05, 83C99 (Secondary) | math.CV astro-ph | Affiliation: | University of Arkansas), Genevra Neumann (Kansas State University | Abstract: | Extending a result from the paper of D. Khavinson and G. Swiatek, we show that the rational harmonic function $ar{r(z)} - z$, 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. | Source: | arXiv, math.CV/0401188 | Services: | Forum | Review | PDF | Favorites |
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