Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772217 | Journal of Functional Analysis | 2017 | 37 Pages |
Abstract
We consider random Gaussian eigenfunctions of the Laplacian on the three-dimensional flat torus, and investigate the number of nodal intersections against a straight line segment. The expected intersection number, against any smooth curve, is universally proportional to the length of the reference curve, times the wavenumber, independent of the geometry. We found an upper bound for the nodal intersections variance, depending on the arithmetic properties of the straight line. The considerations made establish a close relation between this problem and the theory of lattice points on spheres.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Riccardo W. Maffucci,