Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pair correlation of roots of rational functions with rational generating
  functions and quadratic denominators   For any rational functions with complex coefficients $A(z), B(z)$ and $C(z)$,
where $A(z)$, $C(z)$ are not identically zero, we consider the sequence of
rational functions $H_{m}(z)$ with generating function $\sum
H_{m}(z)t^{m}=1/(A(z)t^{2}+B(z)t+C(z))$. We provide an explicit formula for the
limiting pair correlation function of the roots of $\prod_{m=0}^{n}H_{m}(z)$,
as $n\rightarrow\infty$, counting multiplicities, on certain closed subarcs $J$
of a curve $\mathcal{C}$ where the roots lie. We give an example where the
limiting pair correlation function does not exist if $J$ contains the endpoints
of $\mathcal{C}$.

34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex