<abstract xmlns="http://www.w3.org/1999/xhtml"> For an integer b > 1 let (φb(n))n≥0 denote the van der Corput sequence base in b in [0, 1). Answering a question of O. Strauch, C. Aistleitner and M. Hofer showed that the distribution function of (φb(n), φb(n + 1), . . . , φb(n + s − 1))n≥0 on [0, 1)s exists and is a copula. The first and third authors of the present paper showed that this phenomenon extends to a broad class of subsequences of the van der Corput sequence. In this result we extend this paper still further and show that this phenomenon is also true for more general numeration systems based on the beta expansion of W. Parry and A. Rényi.</abstract>

For an integer b > 1 let (φb(n))n≥0 denote the van der Corput sequence base in b in [0, 1). Answering a question of O. Strauch, C. Aistleitner and M. Hofer showed that the distribution function of (φb(n), φb(n + 1), . . . , φb(n + s − 1))n≥0 on [0, 1)s exists and is a copula. The first and third authors of the present paper showed that this phenomenon extends to a broad class of subsequences of the van der Corput sequence. In this result we extend this paper still further and show that this phenomenon is also true for more general numeration systems based on the beta expansion of W. Parry and A. Rényi.

Distribution Functions for Subsequences of Generalized Van Der Corput Sequences

Uniform distribution theory

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Distribution Functions for Subsequences of Generalized Van Der Corput Sequences"}

For an integer b > 1 let (φb(n))n≥0 denote the van der Corput sequence base in b in [0, 1). Answering a question of O. Strauch, C. Aistleitner and M. Hofer...

Distribution Functions for Subsequences of Generalized Van Der Corput Sequences

Published Online: Jan 30, 2018

Page range: 1 - 10

Received: Sep 23, 2015

Accepted: Aug 23, 2016

DOI: https://doi.org/10.1515/udt-2017-0011

Keywords
Generalised van der Corput sequences, beta-expansions, Hartman distributed sequences of integers, distribution functions

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Distribution Functions for Subsequences of Generalized Van Der Corput Sequences

Published Online: Jan 30, 2018

Page range: 1 - 10

Received: Sep 23, 2015

Accepted: Aug 23, 2016

DOI: https://doi.org/10.1515/udt-2017-0011

KeywordsGeneralised van der Corput sequences, beta-expansions, Hartman distributed sequences of integers, distribution functions

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Generalised van der Corput sequences, beta-expansions, Hartman distributed sequences of integers, distribution functions