Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Average Bateman--Horn for Kummer polynomials   For any $r \in \mathbb{N}$ and almost all $k \in \mathbb{N}$ smaller than
$x^r$, we show that the polynomial $f(n) = n^r + k$ takes the expected number
of prime values as $n$ ranges from 1 to $x$. As a consequence, we deduce
statements concerning variants of the Hasse principle and of the integral Hasse
principle for certain open varieties defined by equations of the form
$N_{K/\mathbb{Q}}(\mathbf{z}) = t^r +k \neq 0$ where $K/\mathbb{Q}$ is a
quadratic extension. A key ingredient in our proof is a new large sieve
inequality for Dirichlet characters of exact order $r$.

23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
16
The categories of this paper are: stat