Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectrum is rational in dimension one   A bounded measurable set $\Omega\subset{\mathbb R}^d$ is called a spectral
set if it admits some exponential orthonormal basis $\{e^{2\pi i
\langle\lambda,x\rangle}: \lambda\in\Lambda\}$ for $L^2(\Omega)$. In this
paper, we show that in dimension one $d=1$, any spectrum $\Lambda$ with
$0\in\Lambda$ of a spectral set $\Omega$ with Lebesgue measure normalized to 1
must be rational. Combining previous results that spectrum must be periodic,
the Fuglede's conjecture on ${\mathbb R}^1$ is now equivalent to the
corresponding conjecture on all cyclic groups ${\mathbb Z}_{n}.$

32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc