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Nodal domains of Maass forms, II
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 139, Number 5, October 2017
- pp. 1395-1447
- 10.1353/ajm.2017.0035
- Article
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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 Lindel\"{o}f 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.