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arXiv · 2602.13058

On the multiplicative pair correlations of sums of two squares

Jouni Parkkonen·Frédéric Paulin
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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.

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Jouni Parkkonen, Frédéric Paulin. 2026-02-13. On the multiplicative pair correlations of sums of two squares. https://arxiv.org/abs/2602.13058

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