Arithmetic, zeros, and nodal domains on the sphere

2013/10/29 by Michael Magee, Magee, Michael · 1 citation
Mathematics · #Geometry and complex manifolds #Spectral Theory in Mathematical Physics #Analytic and geometric function theory

paper · pdf · doi:10.48550/arxiv.1310.7977

Abstract

We obtain lower bounds for the number of nodal domains of Hecke eigenfunctions on the sphere. Assuming the generalized Lindelof 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 Lindelof.

Cited by

• The Geodesic Restriction Problem for Arithmetic Spherical Harmonics

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