Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Root sets of polynomials and power series with finite choices of
  coefficients   Given $H\subseteq \mathbb{C}$ two natural objects to study are the set of
zeros of polynomials with coefficients in $H$, $$\{z\in \mathbb{C}: \exists
k>0,\, \exists (a_n)\in H^{k+1}, \sum_{n=0}^{k}a_{n}z^n=0\},$$ and the set of
zeros of power series with coefficients in $H$, $$\{z\in\mathbb{C}: \exists
(a_n)\in H^{\mathbb{N}}, \sum_{n=0}^{\infty} a_nz^n=0\}.$$ In this paper we
consider the case where each element of $H$ has modulus $1$. The main result of
this paper states that for any $r\in(1/2,1),$ if $H$ is
$2\cos^{-1}(\frac{5-4|r|^2}{4})$-dense in $S^1,$ then the set of zeros of
polynomials with coefficients in $H$ is dense in $\{z\in \mathbb{C}: |z|\in
[r,r^{-1}]\},$ and the set of zeros of power series with coefficients in $H$
contains the annulus $\{z\in \mathbb{C}: |z|\in[r,1)\}$. These two statements
demonstrate quantitatively how the set of polynomial zeros/power series zeros
fill out the natural annulus containing them as $H$ becomes progessively more
dense.

25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an