Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Croissance asymptotique de nombres de Weil appartenant \`a un corps de
  nombres fix\'e   We prove an asymptotic formula as $x\to +\infty$ for the number of algebraic
integers $\alpha$ belonging to a fixed CM number field and satisfying
$\alpha\overline{\alpha}\leq x$. This problem is related to the height zeta
function $Z_h(X^K,s)$ associated to the anticanonical class of a certain toric
variety $X^K$ over $\mathbb{Q}$ and we show that $Z_h(X^K,s)$ has a meromorphic
continuation to the half-plane $\{\Re(s)>\frac{1}{2}\}$ where it is holomorphic
except at $s=1$. Along the way we obtain a new proof of Manin's conjecture on
the asymptotic growth of points on $X^K(\mathbb{Q})$ of bounded height.

11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg