In this paper we study the geometric discrepancy of explicit constructions of uniformly distributed
points on the two-dimensional unit sphere. We show that the spherical cap discrepancy …

A deterministic sequence of real numbers in the unit interval is called equidistributed if its
empirical distribution converges to the uniform distribution. Furthermore, the limit distribution of …

The pair correlation is a localized statistic for sequences in the unit interval. Pseudo-random
behavior with respect to this statistic is called Poissonian behavior. The metric theory of pair …

In 2001 Heinrich, Novak, Wasilkowski and Woźniakowski proved that for every s≥1 and N≥1
there exists a sequence (z 1 ,…,z N ) of elements of the s-dimensional unit cube such that …

Let $$\alpha \in (1/2,1)$$ α ∈ ( 1 / 2 , 1 ) be fixed. We prove that $$\begin{aligned} \max _{0 \le
t \le T} |\zeta (\alpha +it)| \ge \exp \left( \frac{c_\alpha (\log T)^{1-\alpha }}{(\log \log T)^\…

In this paper we prove a correspondence principle between multivariate functions of bounded
variation in the sense of Hardy and Krause and signed measures of finite total variation, …

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 …

A classical result of Philipp (1975) states that for any sequence $(n_k) _ {k\geq 1} $ of
integers satisfying the Hadamard gap condition $ n_ {k+ 1}/n_k\ge q> 1\(k= 1, 2,\ldots) $, the …

The problem of finding the largest empty axis-parallel box amidst a point configuration is a
classical problem in computational geometry. It is known that the volume of the largest empty …

In recent years, a variant of the resonance method was developed which allowed to obtain
improved Ω-results for the Riemann zeta function along vertical lines in the critical strip. In the …