Nodal Domains of Maass Forms I

Amit Ghosh, Andre Reznikov, Peter Sarnak

Research output: Contribution to journalArticlepeer-review

49 Scopus citations


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 L2-restrictions of these forms to certain curves on the modular surface. These results, together with the Lindelof Hypothesis and known subconvex L-bounds are applied to prove that locally the number of nodal domains of such a form goes to infinity with its eigenvalue.

Original languageEnglish (US)
Pages (from-to)1515-1568
Number of pages54
JournalGeometric and Functional Analysis
Issue number5
StatePublished - Oct 2013

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology


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