On linear normal lattices configurations

Levin, Mordechay B.; Smorodinsky, Meir

doi:10.5802/jtnb.523

Levin, Mordechay B.¹ ; Smorodinsky, Meir ²

¹ Department of Mathematics Bar-Ilan University 52900, Ramat-Gan, Israel
² School of Mathematical Sciences Tel Aviv University 69978, Tel-Aviv, Israel

Journal de théorie des nombres de Bordeaux, Tome 17 (2005) no. 3, pp. 825-858.

Résumé
Abstract

Dans cet article nous prolongeons la construction de Champernowne de nombres normaux dans la base $b$ pour le cas $ℤ^{d}$ , et obtenons une construction explicite du point générique de la transformation de l’ensemble ${0, 1, . . ., b - 1}^{ℤ^{d}}$ par $ℤ^{d}$ déplacement. Nous prouvons que l’intersection de la configuration de réseau considérée avec une droite arbitraire est une suite normale dans la base $b$ .

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 $b$ .

MR Zbl

DOI : 10.5802/jtnb.523

Affiliations des auteurs :

Levin, Mordechay B. ¹ ; Smorodinsky, Meir ²

¹ Department of Mathematics Bar-Ilan University 52900, Ramat-Gan, Israel
² School of Mathematical Sciences Tel Aviv University 69978, Tel-Aviv, Israel

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Levin, Mordechay B.; Smorodinsky, Meir. On linear normal lattices configurations. Journal de théorie des nombres de Bordeaux, Tome 17 (2005) no. 3, pp. 825-858. doi : 10.5802/jtnb.523. https://www.numdam.org/articles/10.5802/jtnb.523/

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Levin, Mordechay B.; Smorodinsky, Meir On Polynomially Normal Lattice Configurations, Monatshefte für Mathematik, Volume 147 (2006) no. 2, p. 137 | DOI:10.1007/s00605-005-0340-1

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