For a sequence of integers {a(x)} x≥1 we show that the distribution of the pair correlations
of the fractional parts of {<αa(x)>} x≥1 is asymptotically Poissonian for almost all α if the …

We say that a sequence $\{x_n\}_{n \geq 1}$ in $[0,1)$ has Poissonian pair correlations if \begin{equation*}
\lim_{N \rightarrow \infty} \frac{1}{N} \# \left\{ 1 \leq l \neq m \leq N \, : \, \left\…

In this paper we study multivariate integration for a weighted Korobov space for which the
Fourier coefficients of the functions decay exponentially fast. This implies that the functions of …

We say that a sequence ( x n ) n ∈ N in [ 0 , 1 ) has Poissonian pair correlations if lim N →
∞ 1 N # 1 ≤ l ≠ m ≤ N : ‖ x l − x m ‖ ≤ s N = 2 s for every s ≥ 0 . The aim of this article is …

A detailed study of digital (t, m, s)-nets and digital (T,s)-sequences constructed over finite rings
is carried out. We present general existence theorems for digital nets and sequences and …

In recent years the concept of (t, m, s)-nets and of (t, s)-sequences has turned out to be the-
until now-by far most powerful basic concept for the construction of low-discrepancy point …

We present a method to estimate the L 2 -discrepancy of symmetrisized point sets from above
and from below with the help of Walsh series analysis. We apply the method to a class of …

We study the distribution properties of sequences which are a generalization of the well-known
van der Corput–Halton sequences on one hand, and digital (T,s)-sequences on the other…

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 …

The set ${Z_\alpha}:=\{\beta|{\lim _ {n\to\infty}}||{q_n}\beta||= 0\} $ is considered, where ${\left
({{q_n}}\right) _ {n\in {\mathbf {N}}}} $ is the sequence of best approximation denominators …