On linear normal lattices configurations

Mordechay B. Levin, Meir Smorodinsky

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish
Pages (from-to)825-858
Number of pages34
JournalJournal de Theorie des Nombres de Bordeaux
Issue number3
StatePublished - 2005

Bibliographical note

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


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

FundersFunder number
Israel Science Foundation366-172


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