On the number of zeros of certain rational harmonic functions
| dc.creator | Khavinson, Dmitry | |
| dc.creator | Neumann, Genevra | |
| dc.date | 2004-01-15 | |
| dc.date | 2004-03-05 | |
| dc.date.accessioned | 2026-07-07T05:04:35Z | |
| dc.date.available | 2026-07-07T05:04:35Z | |
| dc.description | 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. | |
| dc.description | 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 | |
| dc.identifier | https://arxiv.org/abs/math/0401188 | |
| dc.identifier | http://arxiv.org/abs/math/0401188 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69865 | |
| dc.subject | Complex Variables | |
| dc.subject | Astrophysics | |
| dc.subject | 26C15 (Primary); 30D05, 83C99 (Secondary) | |
| dc.title | On the number of zeros of certain rational harmonic functions | |
| dc.type | text |