Abstract
Let F be an \(L^2\)-normalized Hecke Maaß cusp form for \(\Gamma _0(N) \subseteq {\mathrm{SL}}_{n}({\mathbb {Z}})\) with Laplace eigenvalue \(\lambda _F\). If \(\Omega \) is a compact subset of \(\Gamma _0(N)\backslash {\mathrm{PGL}}_n/\mathrm{PO}_{n}\), we show the bound \(\Vert F|_{\Omega }\Vert _{\infty } \ll _{ \Omega } N^{\varepsilon } \lambda _F^{n(n-1)/8 - \delta }\) for some constant \(\delta = \delta _n> 0\) depending only on n.
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The first author was supported by the Volkswagen Foundation and Starting Grant 258713 of the European Research Council. The second author was supported by Starting Grant 258713 of the European Research Council and OTKA Grant No. NK104183.
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Blomer, V., Maga, P. Subconvexity for sup-norms of cusp forms on \(\mathrm{PGL}(n)\) . Sel. Math. New Ser. 22, 1269–1287 (2016). https://doi.org/10.1007/s00029-015-0219-5
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DOI: https://doi.org/10.1007/s00029-015-0219-5