Nodal Domains of Maass Forms I

By Amit Ghosh, A. Reznikov, Peter Sarnak. 2012

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This paper deals with some questions that have received a lot of attention since they were raised by Hejhal and Rackner in their 1992 numerical computations of Maass forms. We establish sharp upper and lower bounds for the L2-restrictions of these forms to certain curves on the modular surface. These results, together with the Lindelof Hypothesis and known subconvex L∞-bounds are applied to prove that locally the number of nodal domains of such a form goes to infinity with its eigenvalue.

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