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arXiv · 1401.5154

Bounds for eigenforms on arithmetic hyperbolic 3-manifolds

Valentin Blomer·Gergely Harcos·Djordje Milićević
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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.

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Valentin Blomer, Gergely Harcos, Djordje Milićević. 2014-01-21. Bounds for eigenforms on arithmetic hyperbolic 3-manifolds. https://doi.org/10.1215/00127094-3166952

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