On -discrepancy and mixed Monte Carlo and quasi-Monte Carlo sequences.
On integer points in polygons
The phenomenon of anomaly small error terms in the lattice point problem is considered in detail in two dimensions. For irrational polygons the errors are expressed in terms of diophantine properties of the side slopes. As a result, for the -dilatation, , of certain classes of irrational polygons the error terms are bounded as with some , or as with arbitrarily small .
On irregularities of distribution, III
On Irregularities of Distribution in Shifts and Dilations of Integer Sequences. I.
On irregularities of distribution, IV
On irregularities of sums of integers
On normal numbers mod
It is proved that a real-valued function , where I is an interval contained in [0,1), is not of the form with |q(x)|=1 a.e. if I has dyadic endpoints. A relation of this result to the uniform distribution mod 2 is also shown.
On Optimal Extreme-Discrepancy Point Sets in the Square.
On Regularities of the Distribution of Special Sequences.
On some remarkable properties of the two-dimensional Hammersley point set in base 2
We study a special class of -nets in base 2. In particular, we are concerned with the two-dimensional Hammersley net that plays a special role among these since we prove that it is the worst distributed with respect to the star discrepancy. By showing this, we also improve an existing upper bound for the star discrepancy of digital -nets over . Moreover, we show that nets with very low star discrepancy can be obtained by transforming the Hammersley point set in a suitable way.
On the Boundedness of Weyl Sums.
On the corner avoidance properties of various low-discrepancy sequences.
On the diaphony of some finite hybrid point sets
On the discrepancy estimate of normal numbers
On the Discrepancy of Convex Plane Sets.
On the discrepancy of Markov-normal sequences
We construct a Markov normal sequence with a discrepancy of . The estimation of the discrepancy was previously known to be .
On the discrepancy of some hybrid sequences
On the Dispersion Spectrum.
On the distribution of s-dimensional Kronecker-sequences
On the distribution of the sequence (nα) with transcendental α