On exceptional systems of random integers.
On existence and discrepancy of certain digital Niederreiter-Halton sequences
On exponents of convergence of subsequences
On finite pseudorandom binary sequences I: Measure of pseudorandomness, the Legendre symbol
On finite pseudorandom binary sequences III: The Liouville function, I
On finite pseudorandom binary sequences IV: The Liouville function, II
On finite pseudorandom binary sequences VII: The measures of pseudorandomness
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 infinite series representations of real numbers
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 isolated, respectively consecutive large values of arithmetic functions
On (j, ε)-normality in the rational fractions
On (..., k)-Normal Words in Connecting Dynamical Systems.
On Kurzweil's 0-1 law in inhomogeneous Diophantine approximation
We give a necessary and sufficient condition such that, for almost all s ∈ ℝ, ||nθ - s|| < ψ(n) for infinitely many n ∈ ℕ, where θ is fixed and ψ(n) is a positive, non-increasing sequence. This can be seen as a dual result to classical theorems of Khintchine and Szüsz which dealt with the situation where s is fixed and θ is random. Moreover, our result contains several earlier ones as special cases: two old theorems of Kurzweil, a theorem of Tseng and a recent...
On Legendre's theorem related to diophantine approximations