Distribution symmetry of toral eigenfunctions

Martínez, Ángel D.; Torres de Lizaur, Francisco

doi:10.4171/RMI/1324

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Distribution symmetry of toral eigenfunctions

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Torres de Lizaur, Francisco
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.4171/RMI/1324
(Publisher version)

https://doi.org/10.48550/arXiv.2205.14491
(Preprint)

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Martinez-TorresDeLizaur_Distribution symmetry of toral eigenfunctions_2022.pdf
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Citation

Martínez, Á. D., & Torres de Lizaur, F. (2022). Distribution symmetry of toral eigenfunctions. Revista Matemática Iberoamericana, 38(4), 1371-1382. doi:10.4171/RMI/1324.

Cite as: https://hdl.handle.net/21.11116/0000-0009-FF6D-F

Abstract

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.