Geodesic
Hybrid sup-norm bounds for Hecke–Maass cusp forms
Journal of the European Mathematical Society, Tome 17 (2015) no. 8, pp. 2069-2082.

Voir la notice de l'article provenant de la source EMS Press

Let f be a Hecke–Maass cusp form of eigenvalue λ and square-free level N. Normalize the hyperbolic measure such that vol(Y0​(N))=1 and the form f such that ∥f∥2​=1. It is shown that ∥f∥∞​≪ε​λ245​+εN31​+ε for all ε>0. This generalizes simultaneously the current best bounds in the eigenvalue and level aspects.
DOI : 10.4171/jems/550
Classification : 11-XX, 00-XX, 14-XX
Keywords: Automorphic forms, trace formula, amplification, diophantine approximation 
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     author = {Nicolas Templier},
     title = {Hybrid sup-norm bounds for {Hecke{\textendash}Maass} cusp forms},
     journal = {Journal of the European Mathematical Society},
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Nicolas Templier. Hybrid sup-norm bounds for Hecke–Maass cusp forms. Journal of the European Mathematical Society, Tome 17 (2015) no. 8, pp. 2069-2082. doi : 10.4171/jems/550. http://geodesic.mathdoc.fr/articles/10.4171/jems/550/

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