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Arithmetic, Zeros, and Nodal Domains on the Sphere

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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.

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  1. Michael Magee

    Present address: School of Mathematics, Institute for Advanced Study, Princeton, NJ, 08540, USA

Authors and Affiliations

  1. Department of Mathematics, University of California at Santa Cruz, 1156 High Street, Santa Cruz, CA, 95064, USA

    Michael Magee

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  1. Michael Magee
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Correspondence to Michael Magee.

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Communicated by S. Zelditch

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Magee, M. Arithmetic, Zeros, and Nodal Domains on the Sphere. Commun. Math. Phys. 338, 919–951 (2015). https://doi.org/10.1007/s00220-015-2391-z

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