On the sup-norm of Maass cusp forms of large level. III

Abstract

Let $f$ be a Hecke--Maass cuspidal newform of square-free level $N$ and Laplacian eigenvalue $\lambda$. It is shown that $\pnorm{f}_\infty \ll_{λ,ε} N^{-1/6}+ε} \pnorm{f}_2$ for any $\epsilon >0$.

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• $L^4$-norms of Hecke newforms of large level