LARGE VALUES OF CUSP FORMS ON GL n

Farrell Brumley (1) , Nicolas Templier (2)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 Cornell University [New York]

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.

Mots clés: Automorphic forms; Whittaker functions

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

Farrell Brumley, Nicolas Templier. LARGE VALUES OF CUSP FORMS ON GL n. 2014. ⟨hal-01408448⟩