English

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

Spectral Theory 2017-05-23 v1 Number Theory

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(λ2/3)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(λ2/31/495)O(\lambda^{2/3-1/495}).

Keywords

Cite

@article{arxiv.1705.07308,
  title  = {An improved remainder estimate in the Weyl formula for the planar disk},
  author = {Jingwei Guo and Weiwei Wang and Zuoqin Wang},
  journal= {arXiv preprint arXiv:1705.07308},
  year   = {2017}
}