A distributional limit law for the continued fraction digit sum

Details A distributional limit law for the continued fraction digit sum A distributional limit law for the continued fraction digit sum

2005-09-23

arxiv.org/abs/math/0509559v2

Mathematische Nachrichten 281, No. 9, 1294-1306 (2008)

Mathematics

Number Theory

14 pages, 1 figure

Scientific paper

10.1002/mana.200510679

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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