On the discrepancy of two-dimensional perturbed Halton--Kronecker sequences and lacunary trigonometric products
Volume 180 / 2017
Acta Arithmetica 180 (2017), 365-392
MSC: 11K31, 11K38, 11K60.
DOI: 10.4064/aa170505-6-7
Published online: 18 September 2017
Abstract
We consider the star discrepancy of two-dimensional sequences made up as a hybrid between a Kronecker sequence and a perturbed Halton sequence in base 2, where the perturbation is achieved by a digital-sequence construction in the sense of Niederreiter whose generating matrix contains a periodic perturbing sequence of a given period length. Under the assumption that the Kronecker sequence involves a parameter with bounded continued fraction coefficients, sharp discrepancy estimates are obtained. Furthermore, we study the problem from a metric point of view as well. Finally, we also present sharp general and tight metric bounds for certain lacunary trigonometric products which appear to be strongly related to these problems.
