T. Lachmann

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20172021

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5 papers · 1 filter

math.NT2021

On the area of empty axis-parallel rectangles amidst 2-dimensional lattice points

Thomas Lachmann, Jaspar Wiart

The dispersion of a point set in the unit square is defined to be the area of the largest empty axis-parallel box. In this paper we are interested in the dispersion of lattices in…

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.NT2018

The Duffin-Schaeffer conjecture with extra divergence

Christoph Aistleitner, Thomas Lachmann, Marc Munsch +2

The Duffin-Schaeffer conjecture is a fundamental unsolved problem in metric number theory. It asserts that for every non-negative function $ψ : N \to R$ fo…

math.NT2018

There is no Khintchine threshold for metric pair correlations

Christoph Aistleitner, Thomas Lachmann, Niclas Technau

We consider sequences of the form $(a_{n} α)_{n}$ mod 1, where $α \in [0, 1]$ and where $(a_{n})_{n}$ is a strictly increasing sequence of positive in…

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…