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Sup-norm problem of certain eigenfunctions on arithmetic hyperbolic manifolds Jana, Subhajit


We prove a power saving over the local bound for the L∞ norm of uniformly non- tempered Hecke-Maass forms on arithmetic hyperbolic manifolds of dimension 4 and 5. We use accidental isomorphism and use the Hecke theory of the correspond- ing groups to show that if the automorphic form is non-tempered at positive density of finite places then the Hecke eigenvalues are large; amplifying the saving coming from the non temperedness we get a power saving.

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