On linear normal lattices configurations
Journal de Théorie des Nombres de Bordeaux, Tome 17 (2005) no. 3, pp. 825-858.

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 .

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 .

@article{JTNB_2005__17_3_825_0,
     author = {Mordechay B. Levin and Meir Smorodinsky},
     title = {On linear normal lattices configurations},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {825--858},
     publisher = {Universit\'e Bordeaux 1},
     volume = {17},
     number = {3},
     year = {2005},
     doi = {10.5802/jtnb.523},
     zbl = {05016590},
     mrnumber = {2212128},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.523/}
}
Mordechay B. Levin; Meir Smorodinsky. 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://jtnb.centre-mersenne.org/articles/10.5802/jtnb.523/

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