Expected nodal intersection length of random 3D toral eigenfunctions with a plane is proportional to area times wavenumber, with variance upper-bounded via lattice-point estimates on spheres.
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Restriction of 3D arithmetic Laplace eigenfunctions to a plane
Expected nodal intersection length of random 3D toral eigenfunctions with a plane is proportional to area times wavenumber, with variance upper-bounded via lattice-point estimates on spheres.