Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Examples of badly approximable vectors over number fields   We consider approximation of vectors $\mathbf{z}\in
F\otimes\mathbb{R}\cong\mathbb{R}^r\times\mathbb{C}^s$ by elements of a number
field $F$ and construct examples of badly approximable vectors. These examples
come from compact subspaces of $SL_2(\mathcal{O}_F)\backslash
SL_2(F\otimes\mathbb{R})$ naturally associated to (totally indefinite,
anisotropic) $F$-rational binary quadratic and Hermitian forms, a
generalization of the well-known fact that quadratic irrationals are badly
approximable over $\mathbb{Q}$.

18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg