Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Power-free values, large deviations, and integer points on irrational
  curves   Let $f\in \mathbb{Z}\lbrack x\rbrack$ be a polynomial of degree $d\geq 3$
without roots of multiplicity $d$ or $(d-1)$. Erd\H{o}s conjectured that, if
$f$ satisfies the necessary local conditions, then $f(p)$ is free of $(d-1)$th
powers for infinitely many primes $p$. This is proved here for all $f$ with
sufficiently high entropy.
  The proof serves to demonstrate two innovations: a strong repulsion principle
for integer points on curves of positive genus, and a number-theoretical
analogue of Sanov's theorem from the theory of large deviations.

17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics