On the sup-norm of $SL_3$ Hecke–Maass cusp forms

Holowinsky, Roman; Nowland, Kevin; Ricotta, Guillaume; Royer, Emmanuel

doi:10.5802/pmb.36

On the sup-norm of

S L_{3}

Hecke–Maass cusp forms
[Sur la norme infinie des formes de Hecke–Maass de

S L_{3}

]

Holowinsky, Roman ¹ ; Nowland, Kevin ¹ ; Ricotta, Guillaume ² ; Royer, Emmanuel ³

¹ Department of Mathematics, The Ohio State University, 100 Math Tower, 231 West 18th Avenue, Columbus, OH 43210-1174
² Université de Bordeaux, IMB, 351 cours de la libération, 33405 Talence, France
³ Université Blaise Pascal, Laboratoire de mathématiques, Les Cézeaux, BP 80026, 63171 Aubière Cedex, France

Publications mathématiques de Besançon. Algèbre et théorie des nombres, no. 2 (2019), pp. 53-80.

Résumé
Abstract

Ce travail contient une preuve d’une borne non-triviale explicite quantitative par rapport à la valeur propre pour la norme infinie d’une forme de Hecke–Maass cuspidale de $S L_{3} (ℤ)$ restreinte à un ensemble compact.

This work contains a proof of a non-trivial explicit quantitative bound in the eigenvalue aspect for the sup-norm of a $S L_{3} (ℤ)$ Hecke–Maass cusp form restricted to a compact set.

Reçu le : 2018-05-15
Publié le : 2019-12-06

DOI : 10.5802/pmb.36

Classification : 11F55, 11F60, 11F72, 11H55, 11D75, 43A90, 43A80
Mots clés : Automorphic forms, sup-norm, pre-trace formula, amplification method, Paley–Wiener theorem, Helgason transform, spherical function

Affiliations des auteurs :

Holowinsky, Roman ¹ ; Nowland, Kevin ¹ ; Ricotta, Guillaume ² ; Royer, Emmanuel ³

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     title = {On the sup-norm of $SL_3$ {Hecke{\textendash}Maass} cusp forms},
     journal = {Publications math\'ematiques de Besan\c{c}on. Alg\`ebre et th\'eorie des nombres},
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Holowinsky, Roman; Nowland, Kevin; Ricotta, Guillaume; Royer, Emmanuel. On the sup-norm of $SL_3$ Hecke–Maass cusp forms. Publications mathématiques de Besançon. Algèbre et théorie des nombres, no. 2 (2019), pp. 53-80. doi : 10.5802/pmb.36. http://www.numdam.org/articles/10.5802/pmb.36/

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