Year: 2026
Type: preprint
Abstract: We study the distribution of the number of coprime lattice points in randomly translated disks. We prove that its spatial variance is asymptotic to $σ^2r\log r$ and establish a central limit theorem under the corresponding normalization, where $σ^2$ is an explicit positive constant. By truncating the numerators of rational frequencies in lowest terms, the proof reduces higher-moment estimates to counting squarefree denominators in zero-sum relations.
Source: arXiv (Cornell University)
Author: Ji, Xin Hang
Institution: Shanghai Normal University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213307542