Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Szemer\'{e}di-Trotter type theorem in matrix rings and its
  application   In this paper, we study a Szemer\'{e}di-Trotter type theorem in matrix rings.
More precisely, let $\mathcal{P}$ be a set of points and $\mathcal{L}$ be a set
of lines in $M_2(\mathbb{F}_q) \times M_2(\mathbb{F}_q)$, we have \[
I(\mathcal{P},\mathcal{L}) = \left|\left\{ (p,\ell) \in \mathcal{P} \times
\mathcal{L} \,:\, p \in \ell\right\}\right| \leq
\dfrac{|\mathcal{P}||\mathcal{L}|}{q^4} + \sqrt{2}
q^{7/2}\sqrt{|\mathcal{P}||\mathcal{L}|}.\] We also use this theorem to give
other proofs for some recent sum-product type estimates due to Karabulut, Koh,
Pham, Shen, and the second listed author.

11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an