Large deviations for denominators of continued fractions

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

7 pages, 1 figure

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