Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Bohnenblust--Hille inequality for homogeneous polynomials is
  hypercontractive   The Bohnenblust--Hille inequality says that the $\ell^{\frac{2m}{m+1}}$-norm
of the coefficients of an $m$-homogeneous polynomial $P$ on $\C^n$ is bounded
by $\| P\|_\infty$ times a constant independent of $n$, where $\|\cdot
\|_\infty$ denotes the supremum norm on the polydisc $\D^n$. The main result of
this paper is that this inequality is hypercontractive, i.e., the constant can
be taken to be $C^m$ for some $C>1$. Combining this improved version of the
Bohnenblust--Hille inequality with other results, we obtain the following: The
Bohr radius for the polydisc $\D^n$ behaves asymptotically as $\sqrt{(\log
n)/n}$ modulo a factor bounded away from 0 and infinity, and the Sidon constant
for the set of frequencies $\bigl\{\log n: n \text{a positive integer} \le
N\bigr\}$ is $\sqrt{N}\exp\{(-1/\sqrt{2}+o(1))\sqrt{\log N\log\log N}\}$ as
$N\to \infty$.

15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga