English

Points on nodal lines with given direction

Spectral Theory 2018-07-31 v3

Abstract

We study of the directional distribution function of nodal lines for eigenfunctions of the Laplacian on a planar domain. This quantity counts the number of points where the normal to the nodal line points in a given direction. We give upper bounds for the flat torus, and compute the expected number for arithmetic random waves.

Keywords

Cite

@article{arxiv.1802.09603,
  title  = {Points on nodal lines with given direction},
  author = {Zeev Rudnick and Igor Wigman},
  journal= {arXiv preprint arXiv:1802.09603},
  year   = {2018}
}

Comments

The statement and the proof of Theorem 1.2 corrected

R2 v1 2026-06-23T00:34:21.691Z