Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the spectrum of Diophantine approximation constants   The approximation constant $\lambda_{k}(\zeta)$ is defined as the supremum of
real $\eta$ such that $\Vert \zeta^{j}x\Vert\leq x^{-\eta}$ for $1\leq j\leq k$
has infinitely many integer solutions $x$. Here $\Vert.\Vert$ denotes the
distance to the closest integer. We establish a connection on the joint
spectrum $(\lambda_{1}(\zeta),\lambda_{2}(\zeta),\ldots)$ which will lead to
various improvements of known results on the individual spectrum of the
approximation constants $\lambda_{k}(\zeta)$ as well. In particular, this
extends a result by Bugeaud to the case of arbitrary dimension $k$. Concretely,
given $k\geq 1$ and $\lambda\geq 1$, we infer {\em explicit} constructions of
$\zeta$ in the Cantor set with $\lambda_{k}(\zeta)=\lambda$.

26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs