Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improved lower bounds for van der Waerden numbers   Recently, Ben Green proved that the two-color van der Waerden number $w(3,k)$
is bounded from below by $k^{b_0(k)}$ where $b_0(k) = c_0\left(\frac{\log k
}{\log \log k}\right)^{1/3}$. We prove a new lower bound of $k^{b(k)}$ with
$b(k) = \frac{c\log k}{\log \log k}$. This is done by modifying Green's
argument, replacing a complicated result about random quadratic forms with an
elementary probabilistic result.

8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ