An Improved Remainder Estimate in the Weyl Formula for the Planar Disk

作者：Guo, Jingwei; Wang, Weiwei; Wang, Zuoqin^*

来源：Journal of Fourier Analysis and Applications, 2019, 25(4): 1553-1579.

DOI：10.1007/s00041-018-9637-z

• Laplace eigenvalue
• Weyl's law
• Lattice point problem
• Exponential sum

Y. Colin de Verdiere 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 no more than O(mu 2/3). In this paper, we study this problem from spectral geometry by using analysis and number theory. More precisely, by combining with the method of exponential sum estimation, we give a sharper remainder term estimate O(mu 2/3-1/495).

• 出版日期2019-8
• 单位中国科学技术大学