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Communications in Mathematical Physics

, Volume 338, Issue 3, pp 919–951 | Cite as

Arithmetic, Zeros, and Nodal Domains on the Sphere

  • Michael MageeEmail author
Article
  • 169 Downloads

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.

Keywords

Automorphic Form Automorphic Representation Quantum Chaos Nodal Domain Maass Form 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California at Santa CruzSanta CruzUSA
  2. 2.School of MathematicsInstitute for Advanced StudyPrincetonUSA

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