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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…
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…
Effective joint equidistribution of primitive rational points on expanding horospheres
Daniel El-Baz, Bingrong Huang, Min Lee
We prove an effective version of a result due to Einsiedler, Mozes, Shah and Shapira who established the equidistribution of primitive rational points on expanding horospheres in t…
An analogue of the Erdős-Kac theorem for the special linear group over the integers
Daniel El-Baz
We investigate the number of prime factors of individual entries for matrices in the special linear group over the integers. We show that, when properly normalised, it satisfies a…
Spherical equidistribution in adelic lattices and applications
Daniel El-Baz
In this paper we study spherical equidistribution on the space of (translates of) adelic lattices, which we apply to understand the fine-scale statistics of the directions in the s…