The amplification method in the GL(3) Hecke algebra
Publications mathématiques de Besançon. Algèbre et théorie des nombres (2015), pp. 13-40.

This article contains all the technical ingredients required to implement an effective, explicit and unconditional amplifier in the context of GL(3) automorphic forms. In particular, several coset decomposition computations in the GL(3) Hecke algebra are explicitly done.

Cet article contient tous les ingrédients techniques nécessaires à la mise en place efficace, explicite et inconditionnelle de la méthode d’amplification dans le cadre des formes automorphes de GL(3). En particulier, il y est donné plusieurs décompositions explicites de systèmes de représentants dans l’algèbre de Hecke de GL(3).

Published online:
DOI: 10.5802/pmb.11
Classification: 11F99, 11F60, 11F55
Keywords: Amplification method, Hecke operators, Hecke algebras
     author = {Roman Holowinsky and Guillaume Ricotta and Emmanuel Royer},
     title = {The amplification method in the $GL(3)$ {Hecke} algebra},
     journal = {Publications math\'ematiques de Besan\c{c}on. Alg\`ebre et th\'eorie des nombres},
     pages = {13--40},
     publisher = {Presses universitaires de Franche-Comt\'e},
     year = {2015},
     doi = {10.5802/pmb.11},
     zbl = {1380.11053},
     language = {en},
     url = {}
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Roman Holowinsky; Guillaume Ricotta; Emmanuel Royer. The amplification method in the $GL(3)$ Hecke algebra. Publications mathématiques de Besançon. Algèbre et théorie des nombres (2015), pp. 13-40. doi : 10.5802/pmb.11.

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