On the number of zeros of certain rational harmonic functions

Details On the number of zeros of certain rational harmonic functions On the number of zeros of certain rational harmonic functions

2004-01-15

arxiv.org/abs/math/0401188v2

Mathematics

Complex Variables

9 pages, 2 figures; revision discusses applications to gravitational lensing and notes that a result of S. H. Rhie settles the

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

On the number of zeros of certain rational harmonic functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On the number of zeros of certain rational harmonic functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the number of zeros of certain rational harmonic functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-585642