Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bases which admit exactly two expansions   For a positive integer $m$ let $\Omega _m=\{0,1, \cdots , m\}$ and
  \begin{align*}
  \mathcal B_2(m)=&\left \{q\in(1,m+1]: \text{$\exists\; x\in [0, m/(q-1)]$ has
exactly }\right. \\ &\left. \text{two different $q$-expansions w.r.t. $\Omega
_m$}\right \}.
  \end{align*} Sidorov \cite{S} firstly studied the set $\mathcal B_2(1)$ and
raised some questions. Komornik and Kong \cite{KK} further studied the set
$\mathcal B_2(1)$ and answered partial Sidorov's questions. In the present
paper, we consider the set $\mathcal B_2(m)$ for general positive integer $m$
and generalise the results obtained by Komornik and Kong.

36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th