Corpus ID: 119274304

# Traces des op\'erateurs de Hecke sur les espaces de formes automorphes de $\mathrm{SO}_7$, $\mathrm{SO}_8$ ou $\mathrm{SO}_9$ en niveau $1$ et poids arbitraire

@article{Megarbane2016TracesDO,
title={Traces des op\'erateurs de Hecke sur les espaces de formes automorphes de \$\mathrm\{SO\}\_7\$, \$\mathrm\{SO\}\_8\$ ou \$\mathrm\{SO\}\_9\$ en niveau \$1\$ et poids arbitraire},
author={Thomas M'egarban'e},
journal={arXiv: Number Theory},
year={2016}
}
In this article, we determine the trace of some Hecke operators on the spaces of level one automorphic forms on the special orthogonal groups of the euclidean lattices $\mathrm{E}_7$, $\mathrm{E}_8$ and $\mathrm{E}_8\oplus \mathrm{A}_1$, with arbitrary weight. Using Arthur's theory, we deduce properties of the Satake parameters of the automorphic representations for the linear groups discovered by Chenevier and Renard. Our results corroborate a conjecture by Bergstr\"om, Faber and van der Geer… Expand
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