abstract: Let m 3, we prove that (n^ 1) ₍>₀ has Poissonian m-point correlation for all >0, provided <ₘ, where ₘ is an explicit bound which goes to 0 as m increases. This work builds on the method developed in Lutsko-Sourmelidis-Technau (2021), and introduces a new combinatorial argument for higher correlation levels, and new Fourier analytic techniques. A key point is to introduce an `extra' frequency variable to de-correlate the sequence variables and to eventually exploit a repulsion principle for oscillatory integrals. Presently, this is the only positive result showing that the m-point correlation is Poissonian for such sequences.
Lutsko et al. (Tue,) studied this question.