Range-Renewal Structure in Continued Fractions

Jun Wu, Jian-Sheng Xie

Let $\omega =[a_1,a_2,\cdots ]$ be the infinite expansion of continued fraction for an irrational number $\omega \in (0,1)$; let $R_n(\omega )$ (resp. $R_{n,k}(\omega )$, $R_{n,k+}(\omega )$) be the…