Bounds for eigenforms on arithmetic hyperbolic 3-manifolds

Abstract

On a family of arithmetic hyperbolic 3-manifolds of squarefree level, we prove an upper bound for the sup-norm of Hecke-Maass cusp forms, with a power saving over the local geometric bound simultaneously in the Laplacian eigenvalue and the volume. By a novel combination of diophantine and geometric arguments in a noncommutative setting, we obtain bounds as strong as the best corresponding results on arithmetic surfaces.

arXiv comment22 pages, LaTeX2e, to appear in Duke Mathematical Journal

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Cited by in corpus (8)

• Subconvexity for sup-norms of automorphic forms on PGL(n)
• On the sup-norm of SL(3) Hecke-Maass cusp forms
• Theta functions, fourth moments of eigenforms, and the sup-norm problem II
• Beyond the spherical sup-norm problem
• Theta functions, fourth moments of eigenforms, and the sup-norm problem I
• On the global sup-norm of GL(3) cusp forms
• The sup-norm problem for PGL(4)
• Supnorm of an eigenfunction of finitely many Hecke operators