Nodal domains of Maass forms I

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.

To appear in GAFA

References in corpus (3)

• Random wave functions and percolation
• Upper bounds on L-functions at the edge of the critical strip
• Nodal domains of Maass forms II

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