Sharp Hausdorff Dimension Bounds for Sets with Bounded and Growing Digits in $N$-expansions

Andreea Catalina Chitu, Gabriela Ileana Sebe, Dan Lascu

We establish sharp bounds for the Hausdorff dimension of sets of irrational numbers in $(0,1)$ whose digits in the $N$-expansion are either uniformly bounded or tend to infinity. F…