On the multiplicative pair correlations of sums of two squares
Number Theory
2026-02-16 v1
Abstract
We study the pair correlations of the logarithms of the integral values of quadratic norm forms at various scalings, proving the existence of pair correlation measures. We describe a surprising set of asymptotic behaviours when the scaling increases, passing from a punctual measure to a Poissonian behaviour through an exotic behaviour at the transition phase.
Cite
@article{arxiv.2602.13058,
title = {On the multiplicative pair correlations of sums of two squares},
author = {Jouni Parkkonen and Frédéric Paulin},
journal= {arXiv preprint arXiv:2602.13058},
year = {2026}
}
Comments
31 pages, 9 figures