LARGE VALUES OF CUSP FORMS ON GL n

Abstract : We establish lower bounds on the sup norm of Hecke–Maass cusp forms on congruence quotients of GLn(R). The argument relies crucially on uniform estimates for Jacquet-Whittaker functions. These purely local results are of independent interest, and are valid in the more general context of split semi-simple Lie groups. Furthermore, we undertake a fine study of self-dual Jacquet-Whittaker functions on GL3(R), showing that their large values are governed by the Pearcey function.
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Farrell Brumley, Nicolas Templier. LARGE VALUES OF CUSP FORMS ON GL n. 2014. ⟨hal-01408448⟩

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