Geodesic
Hybrid sup-norm bounds for Hecke–Maass cusp forms
Journal of the European Mathematical Society, Tome 17 (2015) no. 8, pp. 2069-2082 Cet article a éte moissonné depuis la source EMS Press

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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 
@article{JEMS_2015_17_8_a4,
     author = {Nicolas Templier},
     title = {Hybrid sup-norm bounds for {Hecke{\textendash}Maass} cusp forms},
     journal = {Journal of the European Mathematical Society},
     pages = {2069--2082},
     year = {2015},
     volume = {17},
     number = {8},
     doi = {10.4171/jems/550},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/550/}
}
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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

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