Variance of Lattice Point Counting in Thin Annuli
Leonardo Colzani, Bianca Gariboldi, Giacomo Gigante
TL;DR
This paper provides asymptotic estimates for the variance in counting integer lattice points within thin annuli across any dimension, enhancing understanding of geometric and number-theoretic distributions.
Contribution
It introduces new asymptotic estimates for the variance of lattice point counts in translated thin annuli in arbitrary dimensions.
Findings
Asymptotic formulas for variance in lattice point counting
Applicability to any dimension
Improved understanding of lattice point distribution
Abstract
We give asymptotic estimates of the variance of the number of integer points in translated thin annuli in any dimension.
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