TY - JOUR

T1 - On a problem of Schweiger concerning normal numbers

AU - Kraaikamp, Cor

AU - Nakada, Hitoshi

N1 - Copyright:
Copyright 2005 Elsevier Science B.V., Amsterdam. All rights reserved.

PY - 2001/2

Y1 - 2001/2

N2 - 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.

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.

KW - Normal numbers

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U2 - 10.1006/jnth.2000.2554

DO - 10.1006/jnth.2000.2554

M3 - Article

AN - SCOPUS:0035255498

VL - 86

SP - 330

EP - 340

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

IS - 2

ER -