On normal numbers for continued fractions

Cor Kraaikamp; Hitoshi Nakada

doi:10.1017/S0143385700000766

On normal numbers for continued fractions

Cor Kraaikamp, Hitoshi Nakada

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1405-1421
Number of pages	17
Journal	Ergodic Theory and Dynamical Systems
Volume	20
Issue number	5
DOIs	https://doi.org/10.1017/S0143385700000766
Publication status	Published - 2000 Oct
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

Access to Document

10.1017/S0143385700000766

Cite this

@article{1b2d99a522484e8bb920c6bf1ace06ff,

title = "On normal numbers for continued fractions",

abstract = "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.",

author = "Cor Kraaikamp and Hitoshi Nakada",

year = "2000",

month = oct,

doi = "10.1017/S0143385700000766",

language = "English",

volume = "20",

pages = "1405--1421",

journal = "Ergodic Theory and Dynamical Systems",

issn = "0143-3857",

publisher = "Cambridge University Press",

number = "5",

}

TY - JOUR

T1 - On normal numbers for continued fractions

AU - Kraaikamp, Cor

AU - Nakada, Hitoshi

PY - 2000/10

Y1 - 2000/10

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0034393949&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034393949&partnerID=8YFLogxK

U2 - 10.1017/S0143385700000766

DO - 10.1017/S0143385700000766

M3 - Article

AN - SCOPUS:0034393949

SN - 0143-3857

VL - 20

SP - 1405

EP - 1421

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 5

ER -

On normal numbers for continued fractions

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this