2017/12/06 by Raman, Sanjay, Schildkraut, Carl
#FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1712.02315
We determine the pair correlations of countable sets T ⊂ ℝn satisfying natural equidistribution conditions. The pair correlations are computed as the volume of a certain region in ℝ2n, which can be expressed in terms of the incomplete Beta function. For n=2 and n=3 we give closed form expressions, and we obtain an expression in the n → ∞ limit. We also verify that sets of lattice points and primitive lattice points satisfy the required distribution criteria.