On the nodal sets of toral eigenfunctions

DOI10.1007/s00222-010-0307-2zbMath1223.58025arXiv1003.1743OpenAlexW3104385371MaRDI QIDQ635853

Jean Bourgain, Ze'ev Rudnick

Publication date: 23 August 2011

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1003.1743

zbMATH Keywords

geodesicshypersurfaceLaplaciannodal setstoral eigenfunctions

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Spectral theory; eigenvalue problems on manifolds (58C40)

Related Items (17)

Ratios of harmonic functions with the same zero set ⋮ Topological properties of Neumann domains ⋮ On logarithmic improvements of critical geodesic restriction bounds in the presence of nonpositive curvature ⋮ Nodal sets of Schrödinger eigenfunctions in forbidden regions ⋮ Courant-sharp eigenvalues of Neumann 2-rep-tiles ⋮ Harmonic functions vanishing on a cone ⋮ Asymptotic distribution of nodal intersections for ARW against a surface ⋮ Nodal length fluctuations for arithmetic random waves ⋮ On the Galois groups of Legendre polynomials ⋮ Nodal intersections and geometric control ⋮ Nodal intersections for random waves on the 3-dimensional torus ⋮ Nodal intersections for random waves against a segment on the 3-dimensional torus ⋮ Restriction of toral eigenfunctions to hypersurfaces and nodal sets ⋮ Control from an interior hypersurface ⋮ Restriction of 3D arithmetic Laplace eigenfunctions to a plane ⋮ Nodal intersections for arithmetic random waves against a surface ⋮ Nodal intersections and \(L^p\) restriction theorems on the torus

Cites Work

• Restrictions of the Laplace-Beltrami eigenfunctions to submanifolds
• Restriction of toral eigenfunctions to hypersurfaces
• Norm form equations. I
• Nodal sets of eigenfunctions on Riemannian manifolds
• Fourier transforms related to convex sets
• New cases of irreducibility for Legendre polynomials. II
• Über Integrale auf konvexen Körpern. I, II
• New cases of irreducibility for Legendre polynomials
• Lp norm estimates of eigenfunctions restricted to submanifolds
• Vanishing sums in function fields
• Diagonal equations over function fields
• Fourier transforms of surface-carried measures and differentiability of surface averages

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