✦ LIBER ✦

On a Problem of Schweiger Concerning Normal Numbers

✍ Scribed by Cor Kraaikamp; Hitoshi Nakada

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 111 KB
Volume: 86
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.2000.2554

No coin nor oath required. For personal study only.

✦ Synopsis

Let T and S be two number theoretical transformations on the n-dimensional unit cube B, and write TtS if there exist positive integers m and n such that T m =S n . F. Schweiger showed in [1969, J. Number Theory 1, 390 397] that TtS implies that every T-normal number x is S-normal. Furthermore, he conjectured that T 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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