FINE-SCALE DISTRIBUTION OF ROOTS OF QUADRATIC CONGRUENCES

被引：2

作者：

Marklof, Jens ^{[1
]}

Welsh, Matthew ^{[1
]}

机构：

[1] Univ Bristol, Sch Math, Bristol, England

来源：

DUKE MATHEMATICAL JOURNAL | 2023年 / 172卷 / 12期

基金：

英国工程与自然科学研究理事会;

关键词：

PAIR CORRELATION; EQUIDISTRIBUTION;

D O I：

10.1215/00127094-2022-0081

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish limit laws for the distribution in small intervals of the roots of the quadratic congruence mu(2) = D mod m, with D > 0 square-free and D (sic) 1 mod 4. This is achieved by translating the problem to convergence of certain geodesic ran-dom 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.

引用

页码：2303 / 2364

页数：62

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