Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $k$-free lattice points in random walks   Let $\mathbb{Z}^2$ be the two-dimensional integer lattice. For an integer
$k\geq 1$, a non-zero lattice point is $k$-free if the greatest common divisor
of its coordinates is a $k$-free number. We consider the proportions of
$k$-free and twin $k$-free lattice points on a path of an $\alpha$-random
walker in $\mathbb{Z}^2$. Using the second-moment method and tools from
analytic number theory, we prove that these two proportions are $1/\zeta(2k)$
and $\prod_{p}(1-2p^{-2k})$, respectively, where $\zeta$ is the Riemann zeta
function and the infinite product takes over all primes.

21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio