论文标题
基地正好承认两个扩展
Bases which admit exactly two expansions
论文作者
论文摘要
对于正整数$ m $ let $ω_m= \ {0,1，\ cdots，m \} $和 \ begin {align*} \ Mathcal b_2（m）=＆\ left \ {q \ in（1，m+1]：\ text {$ \ exists \ exists \; x \ in [0，m/（q-1）] $具有完全} \ right。 \ end {align*} sidorov \ cite {s}首先研究了集合$ \ mathcal b_2（1）$，并提出了一些问题。 Komornik和Kong \ cite {kk}进一步研究了$ \ Mathcal B_2（1）$，并回答了部分Sidorov的问题。在本文中，我们考虑了一般正整数$ m $的集合$ \ Mathcal B_2（M）$，并概括了Komornik和Kong获得的结果。
For a positive integer $m$ let $Ω_m=\{0,1, \cdots , m\}$ 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. $Ω_m$}\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.
