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Nodal Domains of Maass Forms I

Author(s): Ghosh, Amit; Reznikov, Andre; Sarnak, Peter C

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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.
Publication Date: Oct-2013
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
DOI: doi:10.1007/s00039-013-0237-4
ISSN: 1016-443X
Pages: 1515 - 1568
Type of Material: Journal Article
Version: Author's manuscript

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