Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On restricted arithmetic progressions over finite fields   Let A be a subset of $\F_p^n$, the $n$-dimensional linear space over the
prime field $\F_p$ of size at least $\de N$ $(N=p^n)$, and let $S_v=P^{-1}(v)$
be the level set of a homogeneous polynomial map $P:\F_p^n\to\F_p^R$ of degree
$d$, and $v\in\F_p^R$. We show, that under appropriate conditions, the set $A$
contains at least $c\, N|S|$ arithmetic progressions of length $l\leq d$ with
common difference in $S_v$, where c is a positive constant depending on $\de$,
$l$ and $P$. We also show that the conditions are generic for a class of sparse
algebraic sets of density $\approx N^{-\eps}$.

27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con