Nodal domains of maass forms, II

Amit Ghosh; Andre Reznikov; Peter Sarnak

doi:10.1353/ajm.2017.0035

Nodal domains of maass forms, II

Amit Ghosh
, Andre Reznikov
, Peter Sarnak

Department of Mathematics

Oklahoma State University
Princeton University

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

7 Scopus citations

Abstract

In Part I we gave a polynomial growth lower-bound for the number of nodal domains of a Hecke-Maass cuspform in a compact part of the modular surface, assuming a Lindelöf hypothesis. That was a consequence of a topological argument and known subconvexity estimates, together with new sharp lower-bound restriction theorems for the Maass forms. This paper deals with the same question for general (compact or not) arithmetic surfaces which have a reflective symmetry. The topological argument is extended and representation theoretic methods are needed for the restriction theorems, together with results of Waldspurger. Various explicit examples are given and studied.

Original language	English
Pages (from-to)	1395-1447
Number of pages	53
Journal	American Journal of Mathematics
Volume	139
Issue number	5
DOIs	https://doi.org/10.1353/ajm.2017.0035
State	Published - 2017

Bibliographical note

Publisher Copyright:
© 2017 by Johns Hopkins University Press.

Funding

Manuscript received January 3, 2016; revised July 17, 2017. Research of the first author supported in part by IAS, the College of A&S and the Department of Mathematics of his home university, and the Simons Foundation for a Collaboration Grant; research of the second author supported in part by the Veblen Fund at IAS, the ERC grant 291612 and by the ISF grant 533/14; research of the second and third authors supported in part by a BSF grant; research of the third author supported by NSF grant 1302952. American Journal of Mathematics 139 (2017), 1395–1447. ©c 2017 by Johns Hopkins University Press.

Funders	Funder number
National Science Foundation	1302952
Simons Foundation
Bloom's Syndrome Foundation
Iowa Academy of Science
Iowa Science Foundation	533/14
European Commission	291612

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Nodal domains of maass forms, II

Abstract

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