Abstract
We establish limit laws for the distribution in small intervals of the roots of the quadratic congruence μ 2 ≡ D mod m, with D > 0 square-free and D ≢ 1 mod 4. 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.
Original language | English |
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Pages (from-to) | 2303-2364 |
Number of pages | 62 |
Journal | Duke Mathematical Journal |
Volume | 172 |
Issue number | 12 |
Early online date | 1 Sept 2023 |
DOIs | |
Publication status | Published - 12 Oct 2023 |
Bibliographical note
Funding Information:This work was supported by Engineering and Physical Sciences Research Council (EPSRC) grant EP/S024948/1.
Publisher Copyright:
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