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Arithmetic, zeros, and nodal domains on the sphere

Magee, Michael

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Abstract

We obtain lower bounds for the number of nodal domains of Hecke eigenfunctions on the sphere. Assuming the generalized Lindelöf hypothesis we prove that the number of nodal domains of any Hecke eigenfunction grows with the eigenvalue of the Laplacian. By a very different method, we show unconditionally that the average number of nodal domains of degree l Hecke eigenfunctions grows significantly faster than the uniform growth obtained under Lindelöf.

Citation

Magee, M. (2015). Arithmetic, zeros, and nodal domains on the sphere. Communications in Mathematical Physics, 338(3), 919-951. https://doi.org/10.1007/s00220-015-2391-z

Journal Article Type Article
Acceptance Date Mar 2, 2015
Online Publication Date Jun 6, 2015
Publication Date Jun 6, 2015
Deposit Date Sep 7, 2017
Publicly Available Date Mar 29, 2024
Journal Communications in Mathematical Physics
Print ISSN 0010-3616
Electronic ISSN 1432-0916
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 338
Issue 3
Pages 919-951
DOI https://doi.org/10.1007/s00220-015-2391-z

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