JournalsjstVol. 10, No. 3pp. 927–953

Points on nodal lines with given direction

  • Zeév Rudnick

    Tel Aviv University, Israel

  • Igor Wigman

    King's College London, UK
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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.

Cite this article

Zeév Rudnick, Igor Wigman, Points on nodal lines with given direction. J. Spectr. Theory 10 (2020), no. 3, pp. 927–953

DOI 10.4171/JST/317