Subexponentially increasing sums of partial quotients in continued fraction expansions
Subexponentially increasing sums of partial quotients in continued fraction expansions
We investigate from a multifractal analysis point of view the increasing rate of the sums of partial quotients $S\_n(x)=\sum\_{j=1}^n a\_j(x)$, where $x=[a\_1(x), a\_2(x), \cdots ]$ is the continued fraction expansion of an irrational $x\in (0,1)$. Precisely, for an increasing function $\varphi: \mathbb{N} \rightarrow \mathbb{N}$, one is interested in the Hausdorff …