LOWER BOUNDS FOR MAASS FORMS ON SEMISIMPLE GROUPS

Farrell Brumley (1) , Simon Marshall (2)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 Department of Mathematics [Madison]

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.

Mots clés: Automorphic forms; Symmetric varieties

Domaines: Théorie des nombres [math.NT]; Théorie spectrale [math.SP]

Farrell Brumley, Simon Marshall. LOWER BOUNDS FOR MAASS FORMS ON SEMISIMPLE GROUPS. 2016. ⟨hal-01408447⟩