# 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} }

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

The Sup-Norm Problem for PGL(4)

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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). We… Expand

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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.

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We prove a sup norm bound on the real-analytic Eisenstein series, of the form $E(z, 1/2 + iT) \ll T^{3/8 + \varepsilon}$, uniformly for $z$ in a fixed compact subset of $\mathbb{H}$.

The sup-norm problem for GL(2) over number fields

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Let φ be a spherical Hecke–Maaß cusp form on the non-compact space PGL3(ℤ)PGL3(ℝ). We establish various pointwise upper bounds for φ in terms of its Laplace eigenvalue λφ. These imply, for φ… Expand

Explicit subconvexity savings for sup-norms of cusp forms on PGLn(R)

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Abstract Blomer and Maga [2] recently proved that, if F is an L 2 -normalized Hecke-Maass cusp form for SL n ( Z ) , and Ω is a compact subset of PGL n ( R ) / PO n ( R ) , then we have ‖ F | Ω ‖ ∞ ≪… Expand

Lower bounds for Maass forms on semisimple groups

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Let $G$ be an anisotropic semisimple group over a totally real number field $F$. Suppose that $G$ is compact at all but one infinite place $v_{0}$. In addition, suppose that $G_{v_{0}}$ is… Expand

Local analysis of Whittaker new vectors and global applications

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The main focus of this work is the supnorm problem for automorphic forms on GL2, and proves hybrid upper bounds, in other words estimates that are explicit in all major aspects of the Automorphic form under investigation. Expand

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The Sup-Norm Problem for PGL(4)

- Mathematics
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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). We… Expand

Restrictions of SL_3 Maass forms to maximal flat subspaces

- Mathematics
- 2013

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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- 2014

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 coset… Expand

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