On the Independence of Hartman Sequences |
| |
Authors: | J W Sander |
| |
Institution: | Universit?t Hannover, Germany, DE
|
| |
Abstract: | Given and , we define by setting if and only if , where denotes the fractional part of α, i.e. α is considered as an element of the torus . If the topological boundary of A has Haar measure 0, then is called a Hartman sequence, which is a generalisation of Kronecker and Beatty sequences. In this article we answer a question
of Winkler by showing explicitly for which sets , and vectors , we have . The main tool of the proof is Weyl’s theorem on uniform distribution.
Received 3 November 2000; in final form 24 April 2001 |
| |
Keywords: | 2000 Mathematics Subject Classification: 11K36 11K70 28C10 |
本文献已被 SpringerLink 等数据库收录! |
|