Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the number of zeros of certain rational harmonic functions   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.

9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol