4 problems

Let $\mathcal A,\mathcal B\subset\{0,\ldots,M-1\}^2$ be digit sets, let $\mathcal C_{k,\mathcal A}$ and $\mathcal C_{k,\mathcal B}$ be the associated discrete product Cantor sets,…

Higher-dimensional logarithmic-phase FUP conjecture. For each $\nu>0$ there exists $\beta=\beta(\nu)>0$ such that

Generic dilation conjecture. There exists $\beta>\max(0,\frac12-\delta)$ depending only on $\delta$ such that, for a generic choice of $\alpha\in[1,M]$,

Exponential-smallness conjecture. Fix $\delta\in(1/2,1)$. There exists a sequence of pairs $(M_j,\mathcal A_j)$ such that