Result: On normal numbers for continued fractions

Title:
On normal numbers for continued fractions
Authors:
Cor Kraaikamp, Hitoshi Nakada
Source:
Ergodic Theory and Dynamical Systems. 20:1405-1421
Publisher Information:
Cambridge University Press (CUP), 2000.
Publication Year:
2000
Subject Terms:
Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc, Continued fractions and generalizations, Continued fractions, Relations of ergodic theory with number theory and harmonic analysis, nearest integer continued fraction, regular continued fraction, 0101 mathematics, 01 natural sciences, normal numbers, continued fraction from below
Document Type:
Academic journal Article
File Description:
application/xml
Language:
English
ISSN:
1469-4417
0143-3857
DOI:
10.1017/s0143385700000766
Access URL:
https://dialnet.unirioja.es/servlet/articulo?codigo=709844
https://www.cambridge.org/core/journals/ergodic-theory-and-dynamical-systems/article/on-normal-numbers-for-continued-fractions/EC6AC3C112ECEEFC4AB9735A269DA1CA
http://journals.cambridge.org/abstract_S0143385700000766
https://keio.pure.elsevier.com/en/publications/on-normal-numbers-for-continued-fractions
Rights:
Cambridge Core User Agreement
Accession Number:
edsair.doi.dedup.....2e088f6ffd44de1e9fec766e7c39df5f
Database:
OpenAIRE

Further Information

In this paper we will show that any number normal with respect to the regular continued fraction (RCF) is also normal with respect to the continued fraction from below (BCF) and the nearest integer continued fraction (NICF). Furthermore, we will show that in case of the NICF a number is normal with respect to the RCF-expansion if and only if it is NICF-normal. This can be generalized to a larger class of semi-regular continued fraction expansions.