Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discrete restriction for $(x,x^3)$ and related topics   Defining the truncated extension operator $E$ for a sequence $a(n)$ with $n
\in {\mathbb Z}$ by putting \[ E{a}(\alpha,\beta):=\sum_{|n|\leq N}a(n)
e(\alpha n^3 + \beta n), \] we obtain the conjectured tenth moment estimate \[
\| E{a} \|_{L^{10}({\mathbb T}^2)}\lesssim_\epsilon N^{\frac{1}{10}+\epsilon}
\|a\|_{\ell^2({\mathbb Z})}. \] We obtain related conclusions when the curve
$(x,x^3)$ is replaced by $(\phi_1(x), \phi_2(x))$ for suitably independent
polynomials $\phi_1(x),\phi_2(x)$ having integer coefficients.

10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
3
The categories of this paper are: physics
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys