Lattice points and Weyl’s formula for the disc
Acta Arithmetica
MSC: Primary 11P21; Secondary 35P20
DOI: 10.4064/aa230225-6-5
Opublikowany online: 6 June 2024
Streszczenie
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.
