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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 (a)-bounds are applied to prove that locally the number of nodal domains of such a form goes to infinity with its eigenvalue.|
|Electronic Publication Date:||9-Jul-2013|
|Citation:||Ghosh, Amit, Reznikov, Andre, Sarnak, Peter. (2013). Nodal Domains of Maass Forms I. GEOMETRIC AND FUNCTIONAL ANALYSIS, 23 (1515 - 1568. doi:10.1007/s00039-013-0237-4|
|Pages:||1515 - 1568|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||GEOMETRIC AND FUNCTIONAL ANALYSIS|
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