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 to $G$, we prove that there exists a sequence of Laplace eigenfunctions on $Y$ whose sup norms grow like a power of the eigenvalue.

References in corpus (1)

• Large values of newforms on GL(2) with highly ramified central character

Cited by in corpus (2)

• Beyond the spherical sup-norm problem
• Extreme values of geodesic periods on arithmetic hyperbolic surfaces