Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distinct distances on regular varieties over finite fields   In this paper we study some generalized versions of a recent result due to
Covert, Koh, and Pi (2015). More precisely, we prove that if a subset
$\mathcal{E}$ in a regular variety satisfies $|\mathcal{E}|\gg
q^{\frac{d-1}{2}+\frac{1}{k-1}}$, then $\Delta_{k, F}(\mathcal{E})\supseteq
\mathbb{F}_q\setminus \{0\}$ for some certain families of polynomials
$F(\mathbf{x})\in \mathbb{F}_q[x_1, \ldots, x_d]$.

25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess