Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rational points on complete symmetric hypersurfaces over finite fields   For any affine hypersurface defined by a complete symmetric polynomial in
$k\geq 3$ variables of degree $m$ over the finite field $\mathbb{F}_{q}$ of $q$
elements, a special case of our theorem says that this hypersurface has at
least $6q^{k-3}$ rational points over $\mathbb{F}_{q}$ if $1\leq m \leq q-3$
and $q$ is odd. A key ingredient in our proof is Segre's classical theorem on
ovals in finite projective planes.

15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an