Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Compression method and applications   In this paper we introduce and develop the method of compression of points in
space. We introduce the notion of the mass, the rank, the entropy, the cover
and the energy of compression. We leverage this method to prove some class of
inequalities related to Diophantine equations. In particular, we show that for
each $L<n-1$ and for each $K>n-1$, there exist some $(x_1,x_2,\ldots,x_n)\in
\mathbb{N}^n$ with $x_i\neq x_j$ for all $1\leq i<j\leq n$ such that
\begin{align}\frac{1}{K^{n}}\ll \prod \limits_{j=1}^{n}\frac{1}{x_j}\ll
\frac{\log (\frac{n}{L})}{nL^{n-1}}\nonumber \end{align}and that for each
$L>n-1$ there exist some $(x_1,x_2,\ldots,x_n)$ with $x_i\neq x_j$ for all
$1\leq i<j\leq n$ and some $s\geq 2$ such that \begin{align}\sum
\limits_{j=1}^{n}\frac{1}{x_j^s}\gg s\frac{n}{L^{s-1}}.\nonumber \end{align}

32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph