Publications Mathématiques de Besançon

Algèbre et Théorie des Nombres
no. 2
On the sup-norm of SL 3 Hecke–Maass cusp forms
Roman Holowinsky1; Kevin Nowland1; Guillaume Ricotta2; Emmanuel Royer3
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.

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

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 SL 3 (ℤ) restreinte à un ensemble compact.

Received:
Published online:
DOI: 10.5802/pmb.36
Classification: 11F55,  11F60,  11F72,  11H55,  11D75,  43A90,  43A80
Keywords: Automorphic forms, sup-norm, pre-trace formula, amplification method, Paley–Wiener theorem, Helgason transform, spherical function
Roman Holowinsky 1; Kevin Nowland 1; Guillaume Ricotta 2; Emmanuel Royer 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 
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Roman Holowinsky; Kevin Nowland; Guillaume Ricotta; Emmanuel Royer. 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. https://pmb.centre-mersenne.org/articles/10.5802/pmb.36/

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