Arithmetic,Zeros, and Nodal Domains on the Sphere |
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Authors: | Michael Magee |
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Affiliation: | 1.Department of Mathematics,University of California at Santa Cruz,Santa Cruz,USA;2.School of Mathematics,Institute for Advanced Study,Princeton,USA |
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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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