Nodal domains of Maass forms, II

Amit Ghosh, André Reznikov, Peter Sarnak

Type: Article

Publication Date: 2017-01-01

Citations: 13

DOI: https://doi.org/10.1353/ajm.2017.0035

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 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.

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American Journal of Mathematics - View
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+	Twisted symmetric-square L-functions and the nonexistence of Siegel zeros on GL(3)	1997	William D. Banks
+	Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂	2002	Henry Kim
+	Noneuclidean Tesselations and Their Groups	1974	Wilhelm Magnus
+	Automorphic forms and representations	1997	Daniel Bump
+	Rational Quadratic Forms	1982	J. W. S. Cassels
+	Representation theory and automorphic functions	1969	М. И. Граев Ilya Piatetski-Shapiro I. M. Gel'fand K. A. Hirsch
+	Zeros of eigenfunctions on hyperbolic surfaces lying on a curve	2011	Junehyuk Jung
+	Norms of geodesic restrictions for eigenfunctions on hyperbolic surfaces and representation theory	2004	André Reznikov
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+	None	1995	Jeffrey Hoffstein Dinakar Ramakrishnan