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arXiv · 1207.6625

Nodal domains of Maass forms I

Amit Ghosh·Andre Reznikov·Peter Sarnak
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Abstract

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.

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Amit Ghosh, Andre Reznikov, Peter Sarnak. 2013-03-08. Nodal domains of Maass forms I. https://doi.org/10.1007/s00039-013-0237-4

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