On the number of zeros of certain rational harmonic functions
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- by Dmitry Khavinson and Genevra Neumann PDF
- Proc. Amer. Math. Soc. 134 (2006), 1077-1085 Request permission
Abstract:
Extending a result of Khavinson and Świa̧tek (2003) we show that the rational harmonic function $\overline {r(z)} - z$, 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 by Rhie concerning the maximum number of lensed images due to an $n$-point gravitational lens.References
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Additional Information
- Dmitry Khavinson
- Affiliation: Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkansas 72701
- MR Author ID: 101045
- Email: dmitry@uark.edu
- Genevra Neumann
- Affiliation: Department of Mathematics, Kansas State University, Manhattan, Kansas 66506
- Email: neumann@math.ksu.edu
- Received by editor(s): January 22, 2004
- Received by editor(s) in revised form: October 28, 2004
- Published electronically: July 25, 2005
- Additional Notes: The first author was supported by a grant from the National Science Foundation.
- Communicated by: Juha M. Heinonen
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 1077-1085
- MSC (2000): Primary 26C15; Secondary 30D05, 83C99
- DOI: https://doi.org/10.1090/S0002-9939-05-08058-5
- MathSciNet review: 2196041