On a problem of Schweiger concerning normal numbers

Cor Kraaikamp, Hitoshi Nakada

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

Let T and S be two number theoretical transformations on the n-dimensional unit cube B, and write T∼S if there exist positive integers m and n such that Tm=Sn. F. Schweiger showed in [1969, J. Number Theory1, 390-397] that T∼S implies that every T-normal number x is S-normal. Furthermore, he conjectured that T≁S implies that not all T-normal x are S-normal. In this note two counterexamples to this conjecture are given.

Original languageEnglish
Pages (from-to)330-340
Number of pages11
JournalJournal of Number Theory
Volume86
Issue number2
DOIs
Publication statusPublished - 2001 Feb

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Normal number
Imply
Unit cube
Counterexample
n-dimensional
Integer

Keywords

  • Normal numbers

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

On a problem of Schweiger concerning normal numbers. / Kraaikamp, Cor; Nakada, Hitoshi.

In: Journal of Number Theory, Vol. 86, No. 2, 02.2001, p. 330-340.

Research output: Contribution to journalArticle

Kraaikamp, Cor ; Nakada, Hitoshi. / On a problem of Schweiger concerning normal numbers. In: Journal of Number Theory. 2001 ; Vol. 86, No. 2. pp. 330-340.
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