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arXiv · 1012.3843

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

Jean Bourgain·Zeev Rudnick
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Abstract

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.

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Jean Bourgain, Zeev Rudnick. 2011-01-28. On the Geometry of the Nodal Lines of Eigenfunctions of the Two-Dimensional Torus. https://doi.org/10.1007/s00023-011-0098-z

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