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arXiv · 1604.02019

Lower bounds for Maass forms on semisimple groups

Farrell Brumley·Simon Marshall
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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.

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Farrell Brumley, Simon Marshall. 2016-04-07. Lower bounds for Maass forms on semisimple groups. https://doi.org/10.1112/s0010437x20007125

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