Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Vinogradov-type problem in almost primes   We prove a generalisation of Vinogradov's theorem by finding for $m\geqslant
3$ and fixed positive integers $c_1, \dots ,c_m, r_1, \dots , r_m$ the
asymptotics of the number of sequences $(n_1, \dots ,n_m) \in \mathbf{N}^{m}$
such that $c_1n_1 + \dots + c_m n_m = N$ and $\Omega (n_i) = r_i$ for every
$i=1, \dots ,m$ under the assumption that at least three of the $r_i$ are equal
to $1$.

14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci