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arXiv · 1510.02963

Nodal domains of Maass forms II

Amit Ghosh·Andre Reznikov·Peter Sarnak
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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 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.

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Amit Ghosh, Andre Reznikov, Peter Sarnak. 2015-10-10. Nodal domains of Maass forms II. https://doi.org/10.1353/ajm.2017.0035

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