Distribution symmetry of toral eigenfunctions

  • Ángel D. Martínez

    University of Toronto, Canada
  • Francisco Torres de Lizaur

    University of Toronto, Canada
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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.

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Ángel D. Martínez, Francisco Torres de Lizaur, Distribution symmetry of toral eigenfunctions. Rev. Mat. Iberoam. 38 (2022), no. 4, pp. 1371–1382

DOI 10.4171/RMI/1324