Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The density of twins of $k$-free numbers   For $k \geq 2$, we consider the number $A_k(Z)$ of positive integers $n \leq
Z$ such that both $n$ and $n+1$ are $k$-free. We prove an asymptotic formula
$A_k(Z) = c_k Z + O(Z^{14/(9k)+\epsilon})$, where the error term improves upon
previously known estimates. The main tool used is the approximative determinant
method of Heath-Brown.

25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc