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arXiv · 1904.06531

Large deviations for denominators of continued fractions

Hiroki Takahasi
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Abstract

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 $\frac{nπ^2}{12\log2}$. The exponential rate is best possible, given by an analytic function related to the dimension spectrum of Lyapunov exponents for the Gauss transformation.

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Hiroki Takahasi. 2019-04-13. Large deviations for denominators of continued fractions. https://doi.org/10.1088/1361-6544%2Fab9a1d

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