Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantitative bounds for the $U^4$-inverse theorem over low
  characteristic finite fields   This paper gives the first quantitative bounds for the inverse theorem for
the Gowers $U^4$-norm over $\mathbb{F}_p^n$ when $p=2,3$. We build upon earlier
work of Gowers and Mili\'cevi\'c who solved the corresponding problem for
$p\geq 5$. Our proof has two main steps: symmetrization and integration of
low-characteristic trilinear forms. We are able to solve the integration
problem for all $k$-linear forms, but the symmetrization problem we are only
able to solve for trilinear forms. We pose several open problems about
symmetrization of low-characteristic $k$-linear forms whose resolution,
combined with recent work of Gowers and Mili\'cevi\'c, would give quantitative
bounds for the inverse theorem for the Gowers $U^{k+1}$-norm over
$\mathbb{F}_p^n$ for all $k,p$.

28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an