Poisson spacing statistics for lattice points on circles

被引：0
|
作者：
Kurlberg, Par [1 ]
Lester, Stephen [2 ]
机构：
[1] KTH, Dept Math, SE-10044 Stockholm, Sweden
[2] Kings Coll London, Dept Math, London WC2R 2LS, England
来源：
INVENTIONES MATHEMATICAE | 2025年
基金：
瑞典研究理事会; 英国工程与自然科学研究理事会;
关键词：
RANDOM-MATRIX THEORY; RIEMANN ZEROS; ZETA; SUMS;
D O I：
10.1007/s00222-025-01324-1
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that along a density one subsequence of admissible radii, the nearest neighbor spacing between lattice points on circles is Poissonian.
引用
收藏
页码：537 / 585
页数：49
相关论文
共 50 条
  • [1] Lattice points on circles
    Cilleruelo, J
    JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2002, 72 : 217 - 222
  • [2] THE DISTRIBUTION OF THE LATTICE POINTS ON CIRCLES
    CILLERUELO, J
    JOURNAL OF NUMBER THEORY, 1993, 43 (02) : 198 - 202
  • [3] Close Lattice Points on Circles
    Cilleruelo, Javier
    Granville, Andrew
    CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2009, 61 (06): : 1214 - 1238
  • [4] On the Number of Lattice Points in the Shifted Circles
    Jabbarov, Ilgar Sh
    Aslanova, Natiga Sh
    Jeferli, Esmira, V
    AZERBAIJAN JOURNAL OF MATHEMATICS, 2020, 10 (02): : 175 - 190
  • [5] POISSON SPACING STATISTICS FOR VALUE SETS OF POLYNOMIALS
    Kurlberg, Paer
    INTERNATIONAL JOURNAL OF NUMBER THEORY, 2009, 5 (03) : 489 - 513
  • [6] Factors of almost squares and lattice points on circles
    Chan, Tsz Ho
    INTERNATIONAL JOURNAL OF NUMBER THEORY, 2015, 11 (05) : 1701 - 1708
  • [7] On probability measures arising from lattice points on circles
    Kurlberg, Par
    Wigman, Igor
    MATHEMATISCHE ANNALEN, 2017, 367 (3-4) : 1057 - 1098
  • [8] On probability measures arising from lattice points on circles
    Pär Kurlberg
    Igor Wigman
    Mathematische Annalen, 2017, 367 : 1057 - 1098
  • [9] CIRCLES PASSING THROUGH AN ODD NUMBER OF LATTICE POINTS
    BORWEIN, D
    AMERICAN MATHEMATICAL MONTHLY, 1991, 98 (03): : 276 - 277
  • [10] Local Statistics of Lattice Points on the Sphere
    Bourgain, Jean
    Sarnak, Peter
    Rudnick, Zeev
    MODERN TRENDS IN CONSTRUCTIVE FUNCTION THEORY, 2016, 661 : 269 - 282
12345