On the number of zeros of certain rational harmonic functions
Complex Variables
2007-05-23 v2 Astrophysics
Abstract
Extending a result from the paper of D. Khavinson and G. Swiatek, we show that the rational harmonic function , 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.
Keywords
Cite
@article{arxiv.math/0401188,
title = {On the number of zeros of certain rational harmonic functions},
author = {Dmitry Khavinson and Genevra Neumann},
journal= {arXiv preprint arXiv:math/0401188},
year = {2007}
}
Comments
9 pages, 2 figures; revision discusses applications to gravitational lensing and notes that a result of S. H. Rhie settles the question of sharpness of the bound