On a problem of Schweiger concerning normal numbers

Cor Kraaikamp; Hitoshi Nakada

doi:10.1006/jnth.2000.2554

On a problem of Schweiger concerning normal numbers

Cor Kraaikamp, Hitoshi Nakada

Research output: Contribution to journal › Article › peer-review

2 Citations (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 T^m=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 language	English
Pages (from-to)	330-340
Number of pages	11
Journal	Journal of Number Theory
Volume	86
Issue number	2
DOIs	https://doi.org/10.1006/jnth.2000.2554
Publication status	Published - 2001 Feb
Externally published	Yes

Keywords

Normal numbers

ASJC Scopus subject areas

Algebra and Number Theory

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10.1006/jnth.2000.2554

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AB - 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.

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On a problem of Schweiger concerning normal numbers

Abstract

Keywords

ASJC Scopus subject areas

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