JournalsjemsVol. 17, No. 8pp. 2069–2082

Hybrid sup-norm bounds for Hecke–Maass cusp forms

  • Nicolas Templier

    Princeton University, USA
Hybrid sup-norm bounds for Hecke–Maass cusp forms cover
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Abstract

Let ff be a Hecke–Maass cusp form of eigenvalue λ\lambda and square-free level NN. Normalize the hyperbolic measure such that vol(Y0(N))=1\mathrm {vol}(Y_0(N))=1 and the form ff such that f2=1\|{f}\|_2=1. It is shown that fϵλ524+ϵN13+ϵ\|{f}\|_\infty \ll_\epsilon \lambda^{\frac{5}{24}+\epsilon} N^{\frac{1}{3}+\epsilon} for all ϵ>0\epsilon>0. This generalizes simultaneously the current best bounds in the eigenvalue and level aspects.

Cite this article

Nicolas Templier, Hybrid sup-norm bounds for Hecke–Maass cusp forms. J. Eur. Math. Soc. 17 (2015), no. 8, pp. 2069–2082

DOI 10.4171/JEMS/550