Annales Henri Poincaré

, 12:1027 | Cite as

On the Geometry of the Nodal Lines of Eigenfunctions of the Two-Dimensional Torus

  • Jean Bourgain
  • Zeév RudnickEmail author


The width of a convex curve in the plane is the minimal distance between a pair of parallel supporting lines of the curve. In this paper we study the width of nodal lines of eigenfunctions of the Laplacian on the standard flat torus. We prove a variety of results on the width, some having stronger versions assuming a conjecture of Cilleruelo and Granville asserting a uniform bound for the number of lattice points on the circle lying in short arcs.


Lattice Point Trigonometric Polynomial Nodal Line Total Curvature Convex Curve 
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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.School of Mathematics, Institute for Advanced StudyPrincetonUSA
  2. 2.Raymond and Beverly Sackler School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael

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