An improved remainder estimate in the Weyl formula for the planar disk

Abstract

In \cite{colin}, Y. Colin de Verdière proved that the remainder term in the two-term Weyl formula for the eigenvalue counting function for the Dirichlet Laplacian associated with the planar disk is of order $O({\lambda }^{2/3})$. In this paper, by combining with the method of exponential sum estimation, we will give a sharper remainder term estimate $O({\lambda }^{2/3-1/495})$.

References in corpus (1)

• Singularities of the wave trace near cluster points of the length spectrum