Bounds for eigenforms on arithmetic hyperbolic 3-manifolds
Number Theory
2016-05-31 v2
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.
Cite
@article{arxiv.1401.5154,
title = {Bounds for eigenforms on arithmetic hyperbolic 3-manifolds},
author = {Valentin Blomer and Gergely Harcos and Djordje Milićević},
journal= {arXiv preprint arXiv:1401.5154},
year = {2016}
}
Comments
22 pages, LaTeX2e, to appear in Duke Mathematical Journal