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2012

Nodal domains of Maass forms I

Ghosh, Amit, Reznikov, Andre, Sarnak, Peter

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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 $L^2$-restrictions of these forms to certain curves on the modular surface.
These results, together with the Lindelof Hypothesis and known subconvex $L^\infty$-bounds are applied to prove that locally the number of nodal domains of such a form goes to infinity with its eigenvalue.

Nodal domains of Maass forms I · Around

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