17 citations · 73 across the 39 of their papers we have counts for
6 papers · 2 filters
On permutations of lacunary series
Christoph Aistleitner, Istvan Berkes, Robert Tichy
It is a well known fact that for periodic measurable and rapidly increasing the sequence behaves like a sequence of independent, identic…
On the law of the iterated logarithm for permuted lacunary sequences
Christoph Aistleitner, Istvan Berkes, Robert Tichy
It is known that for any smooth periodic function the sequence behaves like a sequence of i.i.d.\ random variables, for example, it satisfies the central l…
On the system and probabilistic number theory
Christoph Aistleitner, Istvan Berkes, Robert Tichy
Let be a measurable function satisfying \begin{equation*} f(x+1)=f(x), \qquad \int_0^1 f(x)\, dx=0, \qquad \int_0^1 f^2(x)\, dx<\infty. \end{equatio…
Low-discrepancy point sets for non-uniform measures
Christoph Aistleitner, Josef Dick
In the present paper we prove several results concerning the existence of low-discrepancy point sets with respect to an arbitrary non-uniform measure on the -dimensional uni…
Metric number theory, lacunary series and systems of dilated functions
Christoph Aistleitner
By a classical result of Weyl, for any increasing sequence of integers the sequence of fractional parts is uniformly distributed modulo…
A note on the Duffin-Schaeffer conjecture with slow divergence
Christoph Aistleitner
For a non-negative function , let denote the set of real numbers for which the inequality has infinitely many coprime solutions $(…