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A distributional limit law for the continued fraction digit sum

by: Marc Kesseböhmer, Mehdi Slassi
(23 Sep 2005)


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We consider the continued fraction digits as random variables measured with respect to Lebesgue measure. The logarithmically scaled and normalized fluctuation process of the digit sums converges strongly distributional to a random variable uniformly distributed on the unit interval. For this process normalized linearly we determine a large deviation asymptotic.


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