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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.|
|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|
|Pages:||1395 - 1447|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||AMERICAN JOURNAL OF MATHEMATICS|
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