On Weyl products and uniform distribution modulo one

In the present paper we study the asymptotic behavior of trigonometric products of the form [Formula: see text] for [Formula: see text] , where the numbers [Formula: see text] are evenly distributed in the unit interval [0, 1]. The main result are matching lower and upper bounds for such products in...

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Autores principales: Aistleitner, Christoph, Larcher, Gerhard, Pillichshammer, Friedrich, Eddin, Sumaia Saad, Tichy, Robert F.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Vienna 2017
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6566311/
https://www.ncbi.nlm.nih.gov/pubmed/31258191
http://dx.doi.org/10.1007/s00605-017-1100-8
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author Aistleitner, Christoph
Larcher, Gerhard
Pillichshammer, Friedrich
Eddin, Sumaia Saad
Tichy, Robert F.
author_facet Aistleitner, Christoph
Larcher, Gerhard
Pillichshammer, Friedrich
Eddin, Sumaia Saad
Tichy, Robert F.
author_sort Aistleitner, Christoph
collection PubMed
description In the present paper we study the asymptotic behavior of trigonometric products of the form [Formula: see text] for [Formula: see text] , where the numbers [Formula: see text] are evenly distributed in the unit interval [0, 1]. The main result are matching lower and upper bounds for such products in terms of the star-discrepancy of the underlying points [Formula: see text] , thereby improving earlier results obtained by Hlawka (Number theory and analysis (Papers in Honor of Edmund Landau, Plenum, New York), 97–118, 1969). Furthermore, we consider the special cases when the points [Formula: see text] are the initial segment of a Kronecker or van der Corput sequences The paper concludes with some probabilistic analogues.
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spelling pubmed-65663112019-06-28 On Weyl products and uniform distribution modulo one Aistleitner, Christoph Larcher, Gerhard Pillichshammer, Friedrich Eddin, Sumaia Saad Tichy, Robert F. Mon Hefte Math Article In the present paper we study the asymptotic behavior of trigonometric products of the form [Formula: see text] for [Formula: see text] , where the numbers [Formula: see text] are evenly distributed in the unit interval [0, 1]. The main result are matching lower and upper bounds for such products in terms of the star-discrepancy of the underlying points [Formula: see text] , thereby improving earlier results obtained by Hlawka (Number theory and analysis (Papers in Honor of Edmund Landau, Plenum, New York), 97–118, 1969). Furthermore, we consider the special cases when the points [Formula: see text] are the initial segment of a Kronecker or van der Corput sequences The paper concludes with some probabilistic analogues. Springer Vienna 2017-09-26 2018 /pmc/articles/PMC6566311/ /pubmed/31258191 http://dx.doi.org/10.1007/s00605-017-1100-8 Text en © The Author(s) 2017 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Aistleitner, Christoph
Larcher, Gerhard
Pillichshammer, Friedrich
Eddin, Sumaia Saad
Tichy, Robert F.
On Weyl products and uniform distribution modulo one
title On Weyl products and uniform distribution modulo one
title_full On Weyl products and uniform distribution modulo one
title_fullStr On Weyl products and uniform distribution modulo one
title_full_unstemmed On Weyl products and uniform distribution modulo one
title_short On Weyl products and uniform distribution modulo one
title_sort on weyl products and uniform distribution modulo one
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6566311/
https://www.ncbi.nlm.nih.gov/pubmed/31258191
http://dx.doi.org/10.1007/s00605-017-1100-8
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