Asymptotics for the spectral function on Zoll manifolds

Let (M,g) be a Zoll manifold, i.e., a smooth, compact, Riemannian manifold without boundary all of whose geodesics are closed with a minimal common period T. The positive definite Laplace-Beltrami operator has eigenvalues \{\lambda_j^2\}_j which cluster around \nu^2_\ell for some sequence \nu_\ell\to \infty. This article is concerned with the number... Show more