Multidimensional sequences uniformly distributed modulo 1 created from normal numbers. (English) Zbl 1356.11045
Cojocaru, A. C. (ed.) et al., SCHOLAR – a scientific celebration highlighting open lines of arithmetic research. Conference in honour of M. Ram Murty’s mathematical legacy on his 60th birthday, Centre de Recherches Mathématiques, Université de Montréal, Canada, October 15–17, 2013. Providence, RI: American Mathematical Society (AMS); Montreal: Centre de Recherches Mathématiques (CRM) (ISBN 978-1-4704-1457-3/pbk; 978-1-4704-2843-3/ebook). Contemporary Mathematics 655. Centre de Recherches Mathématiques Proceedings, 77-82 (2015).
Summary: Let \(q \leq 3\) be a prime number. We create an infinite sequence \(\alpha_1, \alpha_2, \ldots\) of normal numbers in base \(q-1\) such that, for any fixed positive integer \(r\), the \(r\)-dimensional sequence \((\{\alpha_1(q-1)^n\}, \ldots, \{\alpha_r(q-1)^n\})\) is uniformly distributed on \([0,1)^r\).
For the entire collection see [Zbl 1334.11003].
For the entire collection see [Zbl 1334.11003].
MSC:
| 11K36 | Well-distributed sequences and other variations |
| 11K16 | Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. |
| 11J71 | Distribution modulo one |
