Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A lower bound of Ruzsa's number related to the Erd\H{o}s-Tur\'an
  conjecture   For a set $A\subseteq \mathbb{N}$ and $n\in \mathbb{N}$, let $R_A(n)$ denote
the number of ordered pairs $(a,a')\in A\times A$ such that $a+a'=n$. The
celebrated Erd\H{o}s-Tur\'{a}n conjecture says that, if $R_A(n)\ge 1$ for all
sufficiently large integers $n$, then the representation function $R_A(n)$
cannot be bounded. For any positive integer $m$, Ruzsa's number $R_m$ is
defined to be the least positive integer $r$ such that there exists a set
$A\subseteq \mathbb{Z}_m$ with $1\le R_A(n)\le r$ for all $n\in \mathbb{Z}_m$.
In 2008, Chen proved that $R_{m}\le 288$ for all positive integers $m$. In this
paper, we prove that $R_m\ge 6$ for all integers $m\ge 36$. We also determine
all values of $R_m$ when $m\le 35$.

9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
5
The categories of this paper are: gr-qc