Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lattice point visibility on generalized lines of sight   For a fixed $b\in\mathbb{N}=\{1,2,3,\ldots\}$ we say that a point $(r,s)$ in
the integer lattice $\mathbb{Z} \times \mathbb{Z}$ is $b$-visible from the
origin if it lies on the graph of a power function $f(x)=ax^b$ with
$a\in\mathbb{Q}$ and no other integer lattice point lies on this curve (i.e.,
line of sight) between $(0,0)$ and $(r,s)$. We prove that the proportion of
$b$-visible integer lattice points is given by $1/\zeta(b+1)$, where $\zeta(s)$
denotes the Riemann zeta function. We also show that even though the proportion
of $b$-visible lattice points approaches $1$ as $b$ approaches infinity, there
exist arbitrarily large rectangular arrays of $b$-invisible lattice points for
any fixed $b$. This work specialized to $b=1$ recovers original results from
the classical lattice point visibility setting where the lines of sight are
given by linear functions with rational slope through the origin.

35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph