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arXiv · 1701.07979

On the continued fraction expansion of absolutely normal numbers

Adrian-Maria Scheerer
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Abstract

We construct an absolutely normal number whose continued fraction expansion is normal in the sense that it contains all finite patterns of partial quotients with the expected asymptotic frequency as given by the Gauss-Kuzmin measure. The construction is based on ideas of Sierpinski and uses a large deviations theorem for sums of mixing random variables.

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Adrian-Maria Scheerer. 2017-01-27. On the continued fraction expansion of absolutely normal numbers. https://arxiv.org/abs/1701.07979

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