Quantum unique ergodicity and the number of nodal domains of eigenfunctions

Jang, Seung uk; Jung, Junehyuk

doi:10.1090/jams/883

Quantum unique ergodicity and the number of nodal domains of eigenfunctions
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by Seung uk Jang and Junehyuk Jung;

J. Amer. Math. Soc. 31 (2018), 303-318

DOI: https://doi.org/10.1090/jams/883

Published electronically: June 2, 2017

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Abstract:

We prove that the Hecke-Maass eigenforms for a compact arithmetic triangle group have a growing number of nodal domains as the eigenvalue tends to $+\infty$. More generally the same is proved for eigenfunctions on negatively curved surfaces that are even or odd with respect to a geodesic symmetry and for which quantum unique ergodicity holds.

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