Abstract
On a family of arithmetic hyperbolic -manifolds of square-free 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.
Citation
Valentin Blomer. Gergely Harcos. Djordje Milićević. "Bounds for eigenforms on arithmetic hyperbolic -manifolds." Duke Math. J. 165 (4) 625 - 659, 15 March 2016. https://doi.org/10.1215/00127094-3166952
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