We give an exponential upper bound on the probabilitywith which the denominator of the $n$th convergent in the regular continued fraction expansion stays away from the mean $\frac{n\pi^2}{12\log2}$. The exponential rate is best possible, given by an analytic function related to the dimension spectrum of Lyapunov exponents for the Gauss transformation.

中文翻译：

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连分数分母的大偏差

我们给出了规则连分数展开式中第 n$ 个收敛的分母远离均值 $\frac{n\pi^2}{12\log2}$ 的概率的指数上限。指数率是最好的，由与高斯变换的李雅普诺夫指数的维数谱相关的解析函数给出。