Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Short intervals asymptotic formulae for binary problems with prime
  powers   We prove results about the asymptotic formulae in short intervals for the
average number of representations of integers of the forms
$n=p_{1}^{\ell_1}+p_{2}^{\ell_2}$, with $\ell_1, \ell_2\in\{2,3\}$,
$\ell_1+\ell_2\le 5$ are fixed integers, and $n=p^{\ell_1} + m^{\ell_2}$, with
$\ell_1=2$ and $2\le \ell_2\le 11$ or $\ell_1=3$ and $ \ell_2=2$ are fixed
integers,
  $p,p_1,p_2$ are prime numbers and $m$ is an integer.

11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an