Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Density of rational points near/on compact manifolds with certain
  curvature conditions   In this article we establish an asymptotic formula for the number of rational
points, with bounded denominators, within a given distance to a compact
submanifold $\mathcal{M}$ of $\mathbb{R}^M$ with a certain curvature condition.
Our result generalises earlier work of Huang for hypersurfaces [J.-J. Huang,
The density of rational points near hypersurfaces, Duke Math. J. 169 (2020),
2045--2077.], as our curvature condition reduces to Gaussian curvature being
bounded away from $0$ when $M - dim \mathcal{M} = 1$. An interesting feature of
our result is that the asymptotic formula holds beyond the conjectured range of
the distance to $\mathcal{M}$. Furthermore, we obtain an upper bound for the
number of rational points on $\mathcal{M}$ with additional power saving to the
bound in the analogue of Serre's dimension growth conjecture for compact
submanifolds of $\mathbb{R}^M$ when $M - dim \mathcal{M} > 1$.

31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas