Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sum-product estimates via directed expanders   Let $\F_q$ be a finite field of order $q$ and $P$ be a polynomial in
$\F_q[x_1, x_2]$. For a set $A \subset \F_q$, define $P(A):=\{P(x_1, x_2) | x_i
\in A \}$. Using certain constructions of expanders, we characterize all
polynomials $P$ for which the following holds
  \vskip2mm \centerline{\it If $|A+A|$ is small, then $|P(A)|$ is large.}
\vskip2mm
  The case $P=x_1x_2$ corresponds to the well-known sum-product problem.

31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph