Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A variant of the Bombieri-Vinogradov theorem in short intervals with
  applications   We generalize the classical Bombieri-Vinogradov theorem to a short interval,
non-abelian setting. This leads to variants of the prime number theorem for
short intervals where the primes lie in arithmetic progressions that are
"twisted" by a splitting condition in a Galois extension $L/K$ of number
fields. Using this result in conjunction with recent work of Maynard, we prove
that rational primes in short intervals with a given splitting condition in a
Galois extension $L/\mathbb{Q}$ exhibit dense clusters in short intervals. We
explore several arithmetic applications related to questions of Serre regarding
the nonvanishing Fourier coefficients of cuspidal modular forms, including
finding dense clusters of fundamental discriminants $ d $ in short intervals
for which the central values of $d$-quadratic twists of modular $L$-functions
are non-vanishing.

5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol