Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Apollonius circles and irreducibility criteria for polynomials   We prove the irreducibility of integer polynomials $f(X)$ whose roots lie
inside an Apollonius circle associated to two points on the real axis with
integer abscisae $a$ and $b$, with ratio of the distances to these points
depending on the canonical decomposition of $f(a)$ and $f(b)$. In particular,
we obtain irreducibility criteria for the case where $f(a)$ and $f(b)$ have few
prime factors, and $f$ is either an Enestr\"om-Kakeya polynomial, or has a
large leading coefficient. Analogous results are also provided for multivariate
polynomials over arbitrary fields, in a non-Archimedean setting.

3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an