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arXiv · 1904.12554

Explicit subconvexity savings for sup-norms of cusp forms on $\mathrm{PGL}_n(\mathbb R)$

Nate Gillman
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Abstract

Blomer and Maga recently proved that, if $F$ is an $L^2$-normalized Hecke Maass cusp form for $\mathrm{SL}_n(\mathbb Z)$, and $Ω$ is a compact subset of $\mathrm{PGL}_n(\mathbb R)/\mathrm{PO}_n(\mathbb R)$, then we have $\|F|_Ω\|_\infty\ll_Ωλ_F^{n(n-1)/8-δ_n}$ for some $δ_n>0$, where $λ_F$ is the Laplacian eigenvalue of $F$. In the present paper, we prove an explicit version of their result.

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Nate Gillman. 2019-07-14. Explicit subconvexity savings for sup-norms of cusp forms on $\mathrm{PGL}_n(\mathbb R)$. https://doi.org/10.1016/j.jnt.2019.06.002

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