Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Controlling distribution of prime sequences in discretely ordered
  principal ideal subrings of $\mathbb Q[x]$   We show how to construct discretely ordered principal ideal subrings of
$\mathbb Q[x]$ with various types of prime behaviour. Given any set $\mathcal
D$ consisting of finite strictly increasing sequences $(d_1,d_2,\dots, d_l)$ of
positive integers such that, for each prime integer $p$, the set $\{p\mathbb Z,
d_1+p\mathbb Z,\dots, d_l+p\mathbb Z\}$ does not contain all the cosets modulo
$p$, we can stipulate to have, for each $(d_1,\dots, d_l)\in \mathcal D$, a
cofinal set of progressions $(f, f+d_1, \dots, f+d_l)$ of prime elements in our
PID $R_\tau$. Moreover, we can simultaneously guarantee that each positive
prime $g\in R_\tau\setminus\mathbb N$ is either in a prescribed progression as
above or there is no other prime $h$ in $R_\tau$ such that $g-h\in\mathbb Z$.

34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat