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be an anisotropic semisimple group over a totally real number field
. Suppose that
is compact at all but one infinite place
. In addition, suppose that
-almost simple, not split, and has a Cartan involution defined over
is a congruence arithmetic manifold of non-positive curvature associated with
, we prove that there exists a sequence of Laplace eigenfunctions on
whose sup norms grow like a power of the eigenvalue.
We prove a nonvanishing result for families of
-functions in the critical strip, as one factor runs over twists by Hecke characters. As an application, we simplify the proof, due to Luo, Rudnick, and Sarnak, of the best known bounds towards the Generalized Ramanujan Conjecture at the infinite places for cusp forms on
. A key ingredient is the regularization of the units in residue classes by the use of an Arakelov ray class group.
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