Arithmetic, zeros, and nodal domains on the sphere
Number Theory
2015-05-28 v2 Spectral Theory
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.
Cite
@article{arxiv.1310.7977,
title = {Arithmetic, zeros, and nodal domains on the sphere},
author = {Michael Magee},
journal= {arXiv preprint arXiv:1310.7977},
year = {2015}
}
Comments
The final version incorporating referee's comments. To appear in Communications in Mathematical Physics