Abstract
We establish limit laws for the distribution in small intervals of the roots of the quadratic congruence , with square-free and . This is achieved by translating the problem to convergence of certain geodesic random line processes in the hyperbolic plane. This geometric interpretation allows us in particular to derive an explicit expression for the pair correlation density of the roots.
Citation
Jens Marklof. Matthew Welsh. "Fine-scale distribution of roots of quadratic congruences." Duke Math. J. 172 (12) 2303 - 2364, 1 September 2023. https://doi.org/10.1215/00127094-2022-0081
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