Professor Michael Magee michael.r.magee@durham.ac.uk
Professor
Arithmetic, zeros, and nodal domains on the sphere
Magee, Michael
Authors
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 |
Files
Accepted Journal Article
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Copyright Statement
The final publication is available at Springer via https://doi.org/10.1007/s00220-015-2391-z
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