On linear normal lattices configurations
Journal de théorie des nombres de Bordeaux, Volume 17 (2005) no. 3, pp. 825-858.

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

Dans cet article nous prolongeons la construction de Champernowne de nombres normaux dans la base b pour le cas d , et obtenons une construction explicite du point générique de la transformation de l’ensemble {0,1,...,b-1} d par 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 .

DOI: 10.5802/jtnb.523
Mordechay B. Levin 1; Meir Smorodinsky 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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Mordechay B. Levin; Meir Smorodinsky. On linear normal lattices configurations. Journal de théorie des nombres de Bordeaux, Volume 17 (2005) no. 3, pp. 825-858. doi : 10.5802/jtnb.523. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.523/

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