Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Narrow arithmetic progressions in the primes   We study arithmetic progressions in primes with common differences as small
as possible. Tao and Ziegler showed that, for any $k \geq 3$ and $N$ large,
there exist non-trivial $k$-term arithmetic progressions in (any positive
density subset of) the primes up to $N$ with common difference $O((\log
N)^{L_k})$, for an unspecified constant $L_k$. In this work we obtain this
statement with the precise value $L_k = (k-1) 2^{k-2}$. This is achieved by
proving a relative version of Szemer\'{e}di's theorem for narrow progressions
requiring simpler pseudorandomness hypotheses in the spirit of recent work of
Conlon, Fox, and Zhao.

4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg