5 citations · 7 across the 5 of their papers we have counts for
14 papers · 1 filter
On the metric theory of approximations by reduced fractions: a quantitative Koukoulopoulos-Maynard theorem
Christoph Aistleitner, Bence Borda, Manuel Hauke
Let be given. The Duffin-Schaeffer conjecture, recently resolved by Koukoulopoulos and Maynard, asserts that for almost all reals there are infinite…
Difference sets and the metric theory of small gaps
Christoph Aistleitner, Daniel El-Baz, Marc Munsch
Let be a sequence of distinct positive integers. In a recent paper Rudnick established asymptotic upper bounds for the minimal gaps of $\{a_n α\bmod 1, 1 \leq n…
Gap statistics and higher correlations for geometric progressions modulo one
Christoph Aistleitner, Simon Baker, Niclas Technau +1
Koksma's equidistribution theorem from 1935 states that for Lebesgue almost every , the fractional parts of the geometric progression are equidistributed mo…
A pair correlation problem, and counting lattice points with the zeta function
Christoph Aistleitner, Daniel El-Baz, Marc Munsch
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 th…
On the pair correlations of powers of real numbers
Christoph Aistleitner, Simon Baker
A classical theorem of Koksma states that for Lebesgue almost every the sequence is uniformly distributed modulo one. In the present paper we extend Ko…
On the number of gaps of sequences with Poissonian Pair Correlations
Christoph Aistleitner, Thomas Lachmann, Paolo Leonetti +1
A sequence on the torus is said to have Poissonian pair correlations if for all reals , as . It…