Distribution symmetry of toral eigenfunctions

• Ángel D. Martínez ^[1] ; Francisco Torres de Lizaur ^[1]
  1. [1] University of Toronto

     University of Toronto

     Canadá

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº 4, 2022, págs. 1371-1382
• Idioma: inglés
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• Resumen

  • In this paper we study a number of conjectures on the behavior of the value distribution of eigenfunctions. On the two dimensional torus, we observe that the symmetry conjecture holds in the strongest possible sense. On the other hand, we provide a counterexample for higher dimensional tori, which relies on a computer-assisted argument. Moreover we prove a theorem on the distribution symmetry of a certain class of trigonometric polynomials that might be of independent interest.