Arithmetic, zeros, and nodal domains on the sphere

Magee, Michael

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: Jul 10, 2018
• 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