TY - JOUR
T1 - On a problem of Schweiger concerning normal numbers
AU - Kraaikamp, Cor
AU - Nakada, Hitoshi
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
UR - http://www.scopus.com/inward/record.url?scp=0035255498&partnerID=8YFLogxK
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U2 - 10.1006/jnth.2000.2554
DO - 10.1006/jnth.2000.2554
M3 - Article
AN - SCOPUS:0035255498
SN - 0022-314X
VL - 86
SP - 330
EP - 340
JO - Journal of Number Theory
JF - Journal of Number Theory
IS - 2
ER -