On the Geometry of the Nodal Lines of Eigenfunctions of the Two-Dimensional Torus |
| |
Authors: | Jean Bourgain Ze��v Rudnick |
| |
Institution: | 1. School of Mathematics, Institute for Advanced Study, Princeton, NJ, 08540, USA 2. Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, 69978, Tel Aviv, Israel
|
| |
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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|