Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Low-energy decomposition results over finite fields   We prove various low-energy decomposition results, showing that we can
decompose a finite set $A\subset \mathbb{F}_p$ satisfying $|A|<p^{5/8}$, into
$A = S\sqcup T$ so that, for a non-degenerate quadratic $f\in
\mathbb{F}_p[x,y]$, we have
  \[ |\{(s_1,s_2,s_3,s_4)\in S^4 : s_1 + s_2 = s_3 + s_4\}| \ll |A|^{3 -
\frac15 + \varepsilon}
  \] and
  \[
  |\{(t_1,t_2,t_3,t_4)\in T^4 : f(t_1, t_2) = f(t_3, t_4)\}|\ll |A|^{3 -
\frac15 + \varepsilon}\,.
  \]
  Variations include extending this result to large $A$ and a low-energy
decomposition involving additive energy of images of rational functions. This
gives a quantitative improvement to a result of Roche-Newton, Shparlinski and
Winterhof as well as a generalisation of a result of Rudnev, Shkredov and
Stevens.
  We consider applications to conditional expanders, exponential sum estimates
and the finite field Littlewood problem. In particular, we improve results of
Mirzaei, Swaenepoel and Winterhof and Garcia.

9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg