# On the sup-norm of SL 3 Hecke–Maass cusp forms

@article{Holowinsky2014OnTS,
title={On the sup-norm of SL 3 Hecke–Maass cusp forms},
author={Roman Holowinsky and K. Nowland G. Ricotta and Emmanuel Royer},
journal={arXiv: Number Theory},
year={2014}
}
• Published 2014
• Mathematics
• arXiv: Number Theory
This work contains a proof of a non-trivial explicit quantitative bound in the eigenvalue aspect for the sup-norm of a SL(3,Z) Hecke-Maass cusp form restricted to a compact set.
12 Citations

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Let F be a Hecke-Maass cusp form for the group SL(4, Z) with Laplace eigenvalue lambda. Assume that F satisfies the Ramanujan conjecture at infinity (this is satisfied by almost all cusp forms). WeExpand
Restrictions of SL_3 Maass forms to maximal flat subspaces
Let \psi be a Hecke-Maass form on a cubic division algebra over \Q. We apply arithmetic amplification to improve the local bound for the L^2 norm of \psi restricted to maximal flat subspaces.
The amplification method in the GL(3) Hecke algebra
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This article contains all of the technical ingredients required to implement an effective, explicit and unconditional amplifier in the context of GL(3) automorphic forms. In particular, several cosetExpand
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