On normal sets of numbers
On numbers containing each block infinitely often.
On Optimal Extreme-Discrepancy Point Sets in the Square.
On polynomials in primes and J. Bourgain's circle method approach to ergodic theorems II
On pseudorandom binary lattices
On Ramanujan expansions of certain arithmetical functions
On Regularities of the Distribution of Special Sequences.
On Riemann Sums and Lebesgue Integrals.
On Sets Characterizing Additive Arithmetical Functions.
On sets of weak uniform distribution
On some arithmetical properties of middle binomial coefficients
On some Markov matrices arising from the generalized Collatz mapping
On some properties of the Lüroth-type alternating series representations for real numbers.
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 strong uniform distribution
On strong uniform distribution, II. The infinite-dimensional case
We construct infinite-dimensional chains that are L¹ good for almost sure convergence, which settles a question raised in this journal [N]. We give some conditions for a coprime generated chain to be bad for L² or , using the entropy method. It follows that such a chain with positive lower density is bad for . There also exist such bad chains with zero density.
On strong uniform distribution. IV.
On the application of the theory of uniform distribution to the solution of differential equations. (Über die Anwendung der Theorie der Gleichverteilung auf die Lösung von Differentialgleichungen.)
On the arithmetic structure of the integers whose sum of digits is fixed
On the asymptotic distribution of the powers of -matrices