T. Lachmann

activity

20172020

collaborators

3 papers

math.CO2020

The VC-Dimension of Axis-Parallel Boxes on the Torus

Pierre Gillibert, Thomas Lachmann, Clemens Müllner

We show in this paper that the VC-dimension of the family of $d$ -dimensional axis-parallel boxes and cubes on the $d$ -dimensional torus are both asymptotically $d lo g_{2} (d)$ . This…

math.NT2019

On the number of gaps of sequences with Poissonian Pair Correlations

Christoph Aistleitner, Thomas Lachmann, Paolo Leonetti +1

A sequence $(x_{n})$ on the torus is said to have Poissonian pair correlations if $# {1 \leq i \neq = j \leq N : ∣ x_{i} - x_{j} ∣ \leq s / N} = 2 s N (1 + o (1))$ for all reals $s > 0$ , as $N \to \infty$ . It…

math.NT2017

On Exceptional Sets in the Metric Poissonian Pair Correlations problem

Thomas Lachmann, Niclas Technau

Let $(a_{n})_{n}$ be a strictly increasing sequence of positive integers, denote by $A_{N} = {a_{n} : n \leq N}$ its truncations, and let $α\in\left[0,1\righ…