AVERAGE NUMBER OF LATTICE POINTS IN A DISK

作者：Jayakar Sujay^*; Strichartz Robert S^*

来源：Communications on Pure and Applied Analysis, 2016, 15(1): 1-8.

DOI：10.3934/cpaa.2016.15.1

• Lattice points
• Weyl asymptotics
• Bessel function

The difference between the number of lattice points in a disk of radius root t/2 pi and the area of the disk t/4 pi is equal to the error in the Weyl asymptotic estimate for the eigenvalue counting function of the Laplacian on the standard flat torus. We give a sharp asymptotic expression for the average value of the difference over the interval 0 <= t <= R. We obtain similar results for families of ellipses. We also obtain relations to the eigenvalue counting function for the Klein bottle and projective plane.

• 出版日期2016-1