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

Jingwei Guo; Weiwei Wang; Zuoqin Wang

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arXiv · 1705.07308

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

Jingwei Guo·Weiwei Wang·Zuoqin Wang

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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 $O(λ^{2/3})$. 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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Jingwei Guo, Weiwei Wang, Zuoqin Wang. 2017-05-20. An improved remainder estimate in the Weyl formula for the planar disk. https://arxiv.org/abs/1705.07308

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