Large deviations for denominators of continued fractions


الملخص بالإنكليزية

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 $frac{npi^2}{12log2}$. 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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