Lattice points and Weyl’s formula for the disc
Volume 214 / 2024
Acta Arithmetica 214 (2024), 89-107
MSC: Primary 11P21; Secondary 35P20
DOI: 10.4064/aa230225-6-5
Published online: 6 June 2024
Abstract
Following Kuznetsov and Fedosov and Colin de Verdière, we interpret counting eigenvalues of the Laplacian on the unit disc as a lattice point counting problem in analytic number theory. We obtain Weyl’s eigenvalue counting theorem with an area term, a boundary term, and a remainder term as small as that currently known in the Gauss circle problem.
