For a real $x\in(0,1)\setminus\mathbb{Q}$, let $x=[a_1(x),a_2(x),\cdots]$ be
its continued fraction expansion. Denote by $T_n(x):= max \{a_k(x): 1\leq k\leq
n\}$ the leading partial quotient up to $n$. For any real $\alpha\in(0,\infty),
\gamma\in(0,…