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Communications in Mathematical Physics

, Volume 313, Issue 3, pp 791–813 | Cite as

On the Nodal Count for Flat Tori

  • Jochen Brüning
  • David Fajman
Article

Abstract

We give an explicit formula for the number of nodal domains of certain eigenfunctions on a flat torus. We apply this to an isospectral but not isometric family of pairs of flat four-dimensional tori constructed by Conway and Sloane, and we show that corresponding eigenfunctions have the same number of nodal domains. This disproves a conjecture by Brüning, Gnutzmann, and Smilansky.

Keywords

Nodal Count Theta Series Inverse Spectral Problem Nodal Domain Nodal Pattern 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Institut für MathematikHumboldt–UniversitätBerlinGermany
  2. 2.Max Planck Institut for Gravitational Physics (Albert Einstein Institute)GolmGermany

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