On the multiplicative pair correlations of sums of two squares
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.
Fields of Study & Subjects
Analytic Number Theory Research
Mathematical Approximation and Integration
Quantum chaos and dynamical systems
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 13 February 2026
- Language
- EN
- Document type
- Preprint