Arithmetic distributions of convergents arising from Jacobi-Perron algorithm

Valérie Berthé, Hitoshi Nakada, Rie Natsui

Research output: Contribution to journalArticle

Abstract

We study the distribution modulo m of the convergents associated with the d-dimensional Jacobi-Perron algorithm for a.e. real numbers in (0, 1)d by proving the ergodicity of a skew product of the Jacobi-Perron transformation; this skew product was initially introduced in [5] for regular continued fractions.

Original languageEnglish
Pages (from-to)169-185
Number of pages17
JournalIndagationes Mathematicae
Volume17
Issue number2
Publication statusPublished - 2006 Jun 19

Fingerprint

Skew Product
Jacobi
Ergodicity
Continued fraction
Modulo

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Arithmetic distributions of convergents arising from Jacobi-Perron algorithm. / Berthé, Valérie; Nakada, Hitoshi; Natsui, Rie.

In: Indagationes Mathematicae, Vol. 17, No. 2, 19.06.2006, p. 169-185.

Research output: Contribution to journalArticle

Berthé, V, Nakada, H & Natsui, R 2006, 'Arithmetic distributions of convergents arising from Jacobi-Perron algorithm', Indagationes Mathematicae, vol. 17, no. 2, pp. 169-185.
Berthé, Valérie ; Nakada, Hitoshi ; Natsui, Rie. / Arithmetic distributions of convergents arising from Jacobi-Perron algorithm. In: Indagationes Mathematicae. 2006 ; Vol. 17, No. 2. pp. 169-185.
@article{ce8a4f29eb9d416c872ff6325173efcc,
title = "Arithmetic distributions of convergents arising from Jacobi-Perron algorithm",
abstract = "We study the distribution modulo m of the convergents associated with the d-dimensional Jacobi-Perron algorithm for a.e. real numbers in (0, 1)d by proving the ergodicity of a skew product of the Jacobi-Perron transformation; this skew product was initially introduced in [5] for regular continued fractions.",
author = "Val{\'e}rie Berth{\'e} and Hitoshi Nakada and Rie Natsui",
year = "2006",
month = "6",
day = "19",
language = "English",
volume = "17",
pages = "169--185",
journal = "Indagationes Mathematicae",
issn = "0019-3577",
publisher = "Elsevier",
number = "2",

}

TY - JOUR

T1 - Arithmetic distributions of convergents arising from Jacobi-Perron algorithm

AU - Berthé, Valérie

AU - Nakada, Hitoshi

AU - Natsui, Rie

PY - 2006/6/19

Y1 - 2006/6/19

N2 - We study the distribution modulo m of the convergents associated with the d-dimensional Jacobi-Perron algorithm for a.e. real numbers in (0, 1)d by proving the ergodicity of a skew product of the Jacobi-Perron transformation; this skew product was initially introduced in [5] for regular continued fractions.

AB - We study the distribution modulo m of the convergents associated with the d-dimensional Jacobi-Perron algorithm for a.e. real numbers in (0, 1)d by proving the ergodicity of a skew product of the Jacobi-Perron transformation; this skew product was initially introduced in [5] for regular continued fractions.

UR - http://www.scopus.com/inward/record.url?scp=33746931288&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33746931288&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:33746931288

VL - 17

SP - 169

EP - 185

JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

SN - 0019-3577

IS - 2

ER -