Lower bounds for Maass forms on semisimple groups

Abstract

Let $G$ be an anisotropic semisimple group over a totally real number field $F$ . Suppose that $G$ is compact at all but one infinite place $v_{0}$ . In addition, suppose that $G_{v_{0}}$ is $\mathbb{R}$ -almost simple, not split, and has a Cartan involution defined over $F$ . If $Y$ is a congruence arithmetic manifold of non-positive curvature associated with $G$ , we prove that there exists a sequence of Laplace eigenfunctions on $Y$ whose sup norms grow like a power of the eigenvalue.

Locations

• arXiv (Cornell University) - View - PDF
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• Compositio Mathematica - View