Metric properties of continued fractions with large prime partial quotients

Wanjin Cheng, Wen Wu

Let $x\in [0,1)$ with continued fraction expansion $[a_1(x),a_2(x),\dots ]$, and let $\varphi :\mathbb{N}\to {\mathbb{R}}^{+}$ be a non-decreasing function. We consider the numbers whose conti…