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

Speaker: 郭经纬(中国科学技术大学)

Venue: B1044

Time: 2017年12月18日   10:00-11:00

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

Abstract: Y. Colin de Verdiere proved in 2011 that the remainder term is of order $O(lambda^{2/3})$ in the two-term Weyl formula for the eigenvalue counting function for the Dirichlet Laplacian associated with the planar disk. In this talk, we will briefly introduce Colin de Verdiere’s result and method, and then explain how to improve his bound by using harmonic analysis and prove a new bound $O(lambda^{2/3-1/495})$. This problem is closely related to the lattice point problem from number theory.