Full dimensional sets of reals whose sums of partial quotients increase in certain speed

Liangang Ma

For a real $x\in (0,1)\setminus \mathbb{Q}$, let $x=[a_1(x),a_2(x),\cdots ]$ be its continued fraction expansion. Let $s_n(x)={\sum }_{j=1}^n{a}_j(x)$. The Hausdorff dimensions of the lev…