Geodesic
On the discrepancy of two-dimensional perturbed Halton--Kronecker sequences and lacunary trigonometric products
Roswitha Hofer 1   ; Florian Puchhammer 1
1 Institute of Financial Mathematics and Applied Number Theory Johannes Kepler University Linz Altenbergerstraße 69 4040 Linz, Austria
Acta Arithmetica, Tome 180 (2017) no. 4, pp. 365-392 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/aa170505-6-7
Keywords: consider star discrepancy two dimensional sequences made hybrid between kronecker sequence perturbed halton sequence base where perturbation achieved digital sequence construction sense niederreiter whose generating matrix contains periodic perturbing sequence given period length under assumption kronecker sequence involves parameter bounded continued fraction coefficients sharp discrepancy estimates obtained furthermore study problem metric point view finally present sharp general tight metric bounds certain lacunary trigonometric products which appear strongly related these problems

Roswitha Hofer  1   ; Florian Puchhammer  1

1 Institute of Financial Mathematics and Applied Number Theory Johannes Kepler University Linz Altenbergerstraße 69 4040 Linz, Austria 
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     author = {Roswitha Hofer and Florian Puchhammer},
     title = {On the discrepancy of two-dimensional perturbed {Halton--Kronecker} sequences and lacunary trigonometric products},
     journal = {Acta Arithmetica},
     pages = {365--392},
     year = {2017},
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     doi = {10.4064/aa170505-6-7},
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Roswitha Hofer; Florian Puchhammer. On the discrepancy of two-dimensional perturbed Halton--Kronecker sequences and lacunary trigonometric products. Acta Arithmetica, Tome 180 (2017) no. 4, pp. 365-392. doi: 10.4064/aa170505-6-7

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