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

2017/05/20 by Jingwei Guo, Weiwei Wang, Guo, Jingwei +3
Mathematics · Physics and Astronomy · #11P21 #35P20 #FOS: Mathematics #Mathematical functions and polynomials #Number Theory (math.NT) #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1705.07308

openalex publication_date 2017/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In \citecolin, 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(λ^2/3). In this paper, by combining with the method of exponential sum estimation, we will give a sharper remainder term estimate O(λ^2/3-1/495).

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