Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotic $L^4$ norm of polynomials derived from characters   Littlewood investigated polynomials with coefficients in $\{-1,1\}$
(Littlewood polynomials), to see how small their ratio of norms
$||f||_4/||f||_2$ on the unit circle can become as $deg(f)\to\infty$. A small
limit is equivalent to slow growth in the mean square autocorrelation of the
associated binary sequences of coefficients of the polynomials. The
autocorrelation problem for arrays and higher dimensional objects has also been
studied; it is the natural generalization to multivariable polynomials. Here we
find, for each $n > 1$, a family of $n$-variable Littlewood polynomials with
lower asymptotic $||f||_4/||f||_2$ than any known hitherto. We discover these
through a wide survey, infeasible with previous methods, of polynomials whose
coefficients come from finite field characters. This is the first time that the
lowest known asymptotic ratio of norms $||f||_4/||f||_2$ for multivariable
polynomials $f(z_1,...,z_n)$ is strictly less than what could be obtained by
using products $f_1(z_1)... f_n(z_n)$ of the best known univariate polynomials.

20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph