1 results
Lower bounds for Maass forms on semisimple groups
- Part of
-
- Journal:
- Compositio Mathematica / Volume 156 / Issue 5 / May 2020
- Published online by Cambridge University Press:
- 17 April 2020, pp. 959-1003
- Print publication:
- May 2020
-
- Article
- Export citation
-
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.
