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
DOI: 10.4171/RMI/1324
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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.