On the distribution of lattice points in thin annuli

2003/04/09 by C. P. Hughes, Zeév Rudnick, Hughes, C. P. +2
Mathematics · Physics and Astronomy · #Analytic Number Theory Research #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Number Theory (math.NT) #Probability (math.PR) #math-ph #math.MP #math.NT #math.PR

paper · pdf · doi:10.48550/arxiv.math/0304129

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openalex publication_date 2003/04/09 · arxiv created 2003/09/16 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the number of lattice points lying in a thin annulus has a Gaussian value distribution if the width of the annulus tends to zero sufficiently slowly as we increase the inner radius.

Citations

• Level clustering in the regular spectrum

Related

• Statistics of lattice points in thin annuli for generic lattices
• The distribution of lattice points in elliptic annuli
• Variance of Lattice Point Counting in Thin Annuli
• Sparse distribution of lattice points in annular regions
• Some Properties of Annulus SLE