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Quantum unique ergodicity and the number of nodal domains of eigenfunctions


Authors: Seung uk Jang and Junehyuk Jung
Journal: J. Amer. Math. Soc.
MSC (2010): Primary 58J51; Secondary 11F41
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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Additional Information

Seung uk Jang
Affiliation: Center for Applications of Mathematical Principles (CAMP), National Institute for Mathematical Sciences (NIMS), Daejeon 34047, South Korea
Email: seungukj@nims.re.kr

Junehyuk Jung
Affiliation: 360 State Street, New Haven, Connecticut 06510
Email: junehyuk@ias.edu

DOI: https://doi.org/10.1090/jams/883
Received by editor(s): October 29, 2015
Received by editor(s) in revised form: January 13, 2017
Published electronically: June 2, 2017
Additional Notes: The first author was partially supported by the National Institute for Mathematical Sciences (NIMS) grant funded by the Korea government (No. A2320).
The second author was partially supported by the TJ Park Post-doc Fellowship funded by POSCO TJ Park Foundation.
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2013042157) and by the National Science Foundation under agreement No. DMS-1128155.
Article copyright: © Copyright 2017 American Mathematical Society