4 problems

Let $p>q$ be coprime integers. An expansion of a positive real number $x$ in rational base $p/q$ is an infinite word satisfying the rational-base language and valuation conditions…

Let $p>q\geq 1$ be coprime integers and define $T_{p/q}(x)=\left\lceil\frac{p}{q}x\right\rceil$. The rational-base equidistribution conjecture. For every $n\in\mathbb N_{>0}$ and e…

Let $p>q\geq 1$ be coprime integers with $p\leq q^2$. A positive real number $x$ is a $Z_{p/q}$-number if the sequence of fractional parts … is contained in $[0,1/q)$. The generali…

Let $p>q\geq 1$ be coprime integers. An integer expansion is an element $u\in\mathcal{L}_{p/q}$, and let $\mathtt{wmax}_{p/q}(u)$ and $\mathtt{wmin}_{p/q}(u)$ denote the associated…