On the geometry of the nodal lines of eigenfunctions of the two-dimensional torus

DOI10.1007/s00023-011-0098-zzbMath1227.58008arXiv1012.3843OpenAlexW1975495885MaRDI QIDQ639272

Jean Bourgain, Ze'ev Rudnick

Publication date: 20 September 2011

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.3843

zbMATH Keywords

eigenfunctions of the Laplaciannodal linesstandard flat torus

Mathematics Subject Classification ID

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

Related Items (19)

Nodal intersections of random eigenfunctions against a segment on the 2-dimensional torus ⋮ Concentration of the number of intersections of random eigenfunctions on flat tori ⋮ Discrete fractional integrals, lattice points on short arcs, and diophantine approximation ⋮ Linear independence of time-frequency translates in \(\mathbb R^d\) ⋮ Topological properties of Neumann domains ⋮ Planck-scale mass equidistribution of toral Laplace eigenfunctions ⋮ Equidistribution of toral eigenfunctions along hypersurfaces ⋮ Asymptotic distribution of nodal intersections for arithmetic random waves ⋮ Small scale equidistribution for a point scatterer on the torus ⋮ Applications of small-scale quantum ergodicity in nodal sets ⋮ Asymptotic distribution of nodal intersections for ARW against a surface ⋮ Nodal length fluctuations for arithmetic random waves ⋮ Nodal lengths in shrinking domains for random eigenfunctions on \(S^2\) ⋮ CENTRAL LIMIT THEOREM FOR PLANCK‐SCALE MASS DISTRIBUTION OF TORAL LAPLACE EIGENFUNCTIONS ⋮ Planck-scale distribution of nodal length of arithmetic random waves ⋮ Restriction of toral eigenfunctions to hypersurfaces and nodal sets ⋮ A note on distinct distances in rectangular lattices ⋮ Phase singularities in complex arithmetic random waves ⋮ Nodal intersections and \(L^p\) restriction theorems on the torus

Cites Work

• Unnamed Item
• Unnamed Item
• Total curvature of curves in Riemannian manifolds
• Nodal sets of eigenfunctions on Riemannian manifolds
• Eigenfunctions and nodal sets
• A multidimensional version of Turán's Lemma
• On the total curvature of knots
• Close Lattice Points on Circles
• Trigonometric Polynomials and Lattice Points
• ON THE CURVATURE OF THE REAL MILNOR FIBER
• Statistics of nodal lines and points in chaotic quantum billiards: perimeter corrections, fluctuations, curvature
• Arithmetical applications of an identity for the Vandermonde determinant

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