Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An inequality for the norm of a polynomial factor   Let $p(z)$ be a monic polynomial of degree $n$, with complex coefficients,
and let $q(z)$ be its monic factor. We prove an asymptotically sharp inequality
of the form $\|q\|_{E} \le C^n \|p\|_E$, where $\|\cdot\|_E$ denotes the sup
norm on a compact set $E$ in the plane. The best constant $C_E$ in this
inequality is found by potential theoretic methods. We also consider
applications of the general result to the cases of a disk and a segment.

16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int