Nodal Domains of Maass Forms I

Amit Ghosh; Andre Reznikov; Peter Sarnak

doi:10.1007/s00039-013-0237-4

Nodal Domains of Maass Forms I

Amit Ghosh
, Andre Reznikov
, Peter Sarnak

Mathematics

Research output: Contribution to journal › Article › peer-review

52 Scopus citations

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 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 language	English (US)
Pages (from-to)	1515-1568
Number of pages	54
Journal	Geometric and Functional Analysis
Volume	23
Issue number	5
DOIs	https://doi.org/10.1007/s00039-013-0237-4
State	Published - Oct 2013

All Science Journal Classification (ASJC) codes

Analysis
Geometry and Topology

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10.1007/s00039-013-0237-4

Cite this

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author = "Amit Ghosh and Andre Reznikov and Peter Sarnak",

note = "Funding Information: AR and PS thank the BSF grant. All three authors have been partially supported by grant NSFDMS-0554345. AR thanks the ISF Center of Excellency grant 1691/10 and the Veblen Fund at IAS. He was also supported by the ERC grant 291612. AG thanks the Institute for Advanced Study and Princeton University for making possible visits during part of the years 2010-2012 when much of this work took place. He also acknowledges support from the Ellentuck Fund at IAS and the Vaughn Fund at OSU. The software Mathematica{\textcopyright}c was used on a dual-core PC to generate some of the images, using data from [The05].",

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Nodal Domains of Maass Forms I

Abstract

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