Communications in Mathematical Physics

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

On the Nodal Count for Flat Tori

  • Jochen Brüning
  • David Fajman


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.


Nodal Count Theta Series Inverse Spectral Problem Nodal Domain Nodal Pattern 
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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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