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...

Descripción completa

Detalles Bibliográficos
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
Descripción
Sumario: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.

Ejemplares similares