Metric Poissonian pair correlation for real sequences and energy estimates

Abstract

We establish new conditions under which a sequence of real numbers has metric Poissonian pair correlation. These conditions strengthen results of Aistleitner, El-Baz and Munsch (2021) and resolve one of their open problems under a mild growth assumption. As applications, we show that quantitatively convex and polynomial sequences have metric Poissonian pair correlation.

40 pages