Translator Disclaimer
2020 Restriction of 3D arithmetic Laplace eigenfunctions to a plane
Riccardo W. Maffucci
Electron. J. Probab. 25: 1-17 (2020). DOI: 10.1214/20-EJP457

Abstract

We consider a random Gaussian ensemble of Laplace eigenfunctions on the 3D torus, and investigate the 1-dimensional Hausdorff measure (‘length’) of nodal intersections against a smooth 2-dimensional toral sub-manifold (‘surface’). A prior result of ours prescribed the expected length, universally proportional to the area of the reference surface, times the wavenumber, independent of the geometry.

In this paper, for surfaces contained in a plane, we give an upper bound for the nodal intersection length variance, depending on the arithmetic properties of the plane. The bound is established via estimates on the number of lattice points in specific regions of the sphere.

Citation

Download Citation

Riccardo W. Maffucci. "Restriction of 3D arithmetic Laplace eigenfunctions to a plane." Electron. J. Probab. 25 1 - 17, 2020. https://doi.org/10.1214/20-EJP457

Information

Received: 16 September 2019; Accepted: 12 April 2020; Published: 2020
First available in Project Euclid: 8 May 2020

zbMATH: 07225514
MathSciNet: MR4095056
Digital Object Identifier: 10.1214/20-EJP457

Subjects:
Primary: 11P21, 60G15

JOURNAL ARTICLE
17 PAGES


SHARE
Vol.25 • 2020
Back to Top