Arithmetic distributions of convergents arising from Jacobi-Perron algorithm

Valérie Berthé; Hitoshi Nakada; Rie Natsui

doi:10.1016/S0019-3577(06)80014-5

Arithmetic distributions of convergents arising from Jacobi-Perron algorithm

Valérie Berthé, Hitoshi Nakada, Rie Natsui

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

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 language	English
Pages (from-to)	169-185
Number of pages	17
Journal	Indagationes Mathematicae
Volume	17
Issue number	2
DOIs	https://doi.org/10.1016/S0019-3577(06)80014-5
Publication status	Published - 2006 Jun 19
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1016/S0019-3577(06)80014-5

Cite this

@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 = jun,

day = "19",

doi = "10.1016/S0019-3577(06)80014-5",

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

U2 - 10.1016/S0019-3577(06)80014-5

DO - 10.1016/S0019-3577(06)80014-5

M3 - Article

AN - SCOPUS:33746931288

SN - 0019-3577

VL - 17

SP - 169

EP - 185

JO - Indagationes Mathematicae

JF - Indagationes Mathematicae

IS - 2

ER -

Arithmetic distributions of convergents arising from Jacobi-Perron algorithm

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this