Nodal domains of maass forms, II

Amit Ghosh, Andre Reznikov, Peter Sarnak

Research output: Contribution to journalArticle

3 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 languageEnglish (US)
Pages (from-to)1395-1447
Number of pages53
JournalAmerican Journal of Mathematics
Volume139
Issue number5
DOIs
StatePublished - Jan 1 2017

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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