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

Published 20 May 2017 in math.SP and math.NT | (1705.07308v1)

Abstract: In \cite{colin}, Y. Colin de Verdi`ere 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 $O(\lambda^{{2/3-1/495})$.}