Fine-scale distribution of roots of quadratic congruences

Jens Marklof, Matthew C Welsh

Research output: Contribution to journalArticle (Academic Journal)peer-review

1 Citation (Scopus)
30 Downloads (Pure)

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 languageEnglish
Pages (from-to)2303-2364
Number of pages62
JournalDuke Mathematical Journal
Volume172
Issue number12
Early online date1 Sept 2023
DOIs
Publication statusPublished - 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:
© 2023 Duke University Press. All rights reserved.

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