The sup-norm problem for automorphic cusp forms of PGL(n,ℤ[i])

2023/01/11 by Maga, Péter, Zábrádi, Gergely
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2301.04405

Abstract

Let ϕ be an L²-normalized Hecke--Maaß cusp form for PGL_n(ℤ[i]) on the locally symmetric space X:=PGL_n(ℤ[i])\backslash PGL_n(ℂ) / PU_n. If Ω is a compact subset of X, then we prove the bound ‖ϕ|_Ω‖_∞≪_Ω λ_ϕ^n(n-1)/4-δ for some δ>0 depending only on n, where λ_ϕ is the Laplace eigenvalue of ϕ.

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