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NODAL DOMAINS OF MAASS FORMS, II

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

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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 LindeRif 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.
Publication Date: Oct-2017
Electronic Publication Date: Oct-2017
Citation: Ghosh, Amit, Reznikov, Andre, Sarnak, Peter. (2017). NODAL DOMAINS OF MAASS FORMS, II. AMERICAN JOURNAL OF MATHEMATICS, 139 (1395 - 1447. doi:10.1353/ajm.2017.0035
DOI: doi:10.1353/ajm.2017.0035
ISSN: 0002-9327
EISSN: 1080-6377
Pages: 1395 - 1447
Type of Material: Journal Article
Journal/Proceeding Title: AMERICAN JOURNAL OF MATHEMATICS
Version: Author's manuscript



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