47 citations · 331 across the 35 of their papers we have counts for
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Extreme and periodic discrepancy of plane point sets
Aicke Hinrichs, Ralph Kritzinger, Friedrich Pillichshammer
In this paper we study the extreme and the periodic discrepancy of plane point sets. The extreme discrepancy is based on arbitrary rectangles as test sets whereas the periodi…
A note on the periodic -discrepancy of Korobov's -sets
Josef Dick, Aicke Hinrichs, Friedrich Pillichshammer
We study the periodic -discrepancy of point sets in the -dimensional torus. This discrepancy is intimately connected with the root-mean-square -discrepancy of shifted…
On a multi-dimensional Poissonian pair correlation concept and uniform distribution
Aicke Hinrichs, Lisa Kaltenböck, Gerhard Larcher +2
The aim of the present article is to introduce a concept which allows to generalise the notion of Poissonian pair correlation, a second-order equidistribution property, to higher d…
Discrepancy of second order digital sequences in function spaces with dominating mixed smoothness
Josef Dick, Aicke Hinrichs, Lev Markhasin +1
The discrepancy function measures the deviation of the empirical distribution of a point set in from the uniform distribution. In this paper, we study the classical discr…
Optimal -discrepancy bounds for second order digital sequences
Josef Dick, Aicke Hinrichs, Lev Markhasin +1
The -discrepancy is a quantitative measure for the irregularity of distribution modulo one of infinite sequences. In 1986 Proinov proved for all a lower bound for the $L…
Optimal order of -discrepancy of digit shifted Hammersley point sets in dimension 2
Aicke Hinrichs, Ralph Kritzinger, Friedrich Pillichshammer
It is well known that the two-dimensional Hammersley point set consisting of elements (also known as Roth net) does not have optimal order of -discrepancy for $p \in (…