Pólya's conjecture for Dirichlet eigenvalues of annuli
Abstract
Abstract We prove Pólya's conjecture for the eigenvalues of the Dirichlet Laplacian on annular domains. Our approach builds upon and extends the methods we previously developed for disks and balls. It combines variational bounds, estimates of Bessel phase functions, refined lattice point counting techniques and a rigorous computer‐assisted analysis. As a by‐product, we also derive a two‐term upper bound for the Dirichlet eigenvalue counting function of the disk, improving upon Pólya's original estimate.
Fields of Study & Subjects
Analytic and geometric function theory
Spectral Theory in Mathematical Physics
Geometry and complex manifolds
Publication details
- Journal / source
- Journal of the London Mathematical Society
- Publisher
- Wiley
- Volume
- 113
- Issue
- 2
- Publication date
- 1 February 2026
- Language
- EN