Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the normalized arithmetic Hilbert function   Let $X$ be a subvariety of dimension n of the projective space over
$\overline{\mathbb{Q}}$, and $H_{norm}(X;D)$ the normalized arithmetic Hilbert
function of $X$ introduced by Philippon and Sombra. We show that this function
admits the following asymptotic expansion $H_{norm}(X;D) =
\frac{\widehat{h}(X)}{(n + 1)!}D^{n+1} + o(D^{n+1})$ where $\widehat{h}(X)$ is
the normalized height of $X$. This gives a positive answer to a question raised
by Philippon and Sombra.

36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci