On linear normal lattices configurations

Mordechay B. Levin; Meir Smorodinsky

doi:10.5802/jtnb.523

On linear normal lattices configurations

Mordechay B. Levin, Meir Smorodinsky

Department of Mathematics

Tel Aviv University

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

1 Scopus citations

Abstract

In this paper we extend Champernowne’s construction of normal numbers in base b to the ℤ^d case and obtain an explicit construction of the generic point of the ℤ^d shift transformation of the set {0, 1, ..., b−1}ℤ^d . We prove that the intersection of the considered lattice configuration with an arbitrary line is a normal sequence in base b.

Original language	English
Pages (from-to)	825-858
Number of pages	34
Journal	Journal de Theorie des Nombres de Bordeaux
Volume	17
Issue number	3
DOIs	https://doi.org/10.5802/jtnb.523
State	Published - 2005

Bibliographical note

Publisher Copyright:
© Université Bordeaux 1, 2005, tous droits réservés.

Funding

Work supported in part by the Israel Science Foundation Grant No. 366-172.

Funders	Funder number
Israel Science Foundation	366-172

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10.5802/jtnb.523

Cite this

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AB - In this paper we extend Champernowne’s construction of normal numbers in base b to the ℤd case and obtain an explicit construction of the generic point of the ℤd shift transformation of the set {0, 1, ..., b−1}ℤd . We prove that the intersection of the considered lattice configuration with an arbitrary line is a normal sequence in base b.

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On linear normal lattices configurations

Abstract

Bibliographical note

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