On polynomially normal lattice configurations

Mordechay B. Levin, Meir Smorodinsky

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

In this paper we extend Champernowne's construction of a normal sequence in base b to the ℕ2 case and obtain an explicit construction of the generic point of the ℕ2 shift transformation of the set {0,1,...,b-1}ℕ2. We prove that the intersection of the constructed configuration with an arbitrary polynomial curve in the plane is a normal sequence in base b.

Original languageEnglish
Pages (from-to)137-153
Number of pages17
JournalMonatshefte fur Mathematik
Volume147
Issue number2
DOIs
StatePublished - Jan 2006

Keywords

  • Normal numbers
  • Uniform distribution

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