Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The convergence of a sequence of polynomials and the distribution of
  their zeros   Suppose that $\langle f_n \rangle$ is a sequence of polynomials, $\langle
f_n^{(k)}(0)\rangle$ converges for every non-negative integer $k$, and that the
limit is not $0$ for some $k$. It is shown that if all the zeros of $f_1, f_2,
\dots$ lie in the closed upper half plane $\rm{Im}\ z\geq 0$, or if $f_1, f_2,
\dots$ are real polynomials and the numbers of their non-real zeros are
uniformly bounded, then the sequence converges uniformly on compact sets in the
complex plane. The results imply a theorem of Benz and a conjecture of P\'olya.

5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga