A distributional limit law for the continued fraction digit sum
Number Theory
2010-12-24 v2 Dynamical Systems
Abstract
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.
Cite
@article{arxiv.math/0509559,
title = {A distributional limit law for the continued fraction digit sum},
author = {Marc Kesseböhmer and Mehdi Slassi},
journal= {arXiv preprint arXiv:math/0509559},
year = {2010}
}
Comments
14 pages, 1 figure