On the continued fraction expansion of absolutely normal numbers

2017/01/27 by Adrian-Maria Scheerer, Scheerer, Adrian-Maria · 2 citations
Computer Science · Mathematics · #11K16 (Primary) 11Y65 #60F10 (Secondary) #Cellular Automata and Applications #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1701.07979

openalex publication_date 2017/01/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Transcendence Meets Normality: Construction of Transcendentally Normal Numbers
• On the Borel complexity of continued fraction normal, absolutely\n abnormal numbers

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