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 v0 is 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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Submitted on : Sunday, December 4, 2016 - 11:26:16 PM
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Farrell Brumley, Simon Marshall. LOWER BOUNDS FOR MAASS FORMS ON SEMISIMPLE GROUPS. 2016. ⟨hal-01408447⟩

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