Odometers and systems of numeration
On a form of the Erdős-Turán inequality
On a Problem of Erdös in the Theory of Irregularities of Distribution.
On a problem of K. F. Roth concerning irregularities of point distribution.
On a problem of W. M. Schmidt concerning one-sided ireegularities of point distrubitions.
On absolute (j, ε)-normality in the rational fractions with applications to normal numbers
On existence and discrepancy of certain digital Niederreiter-Halton sequences
On functions with bounded remainder
Let be a von Neumann-Kakutani - adic adding machine transformation and let . PutWe study three questions:1. When will be bounded?2. What can be said about limit points of 3. When will the skew product be ergodic on
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.