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Arithmetic, zeros, and nodal domains on the sphere.

Magee, Michael (2015) 'Arithmetic, zeros, and nodal domains on the sphere.', Communications in mathematical physics., 338 (3). pp. 919-951.

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.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1007/s00220-015-2391-z
Publisher statement:The final publication is available at Springer via https://doi.org/10.1007/s00220-015-2391-z
Date accepted:02 March 2015
Date deposited:10 July 2018
Date of first online publication:06 June 2015
Date first made open access:No date available

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