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arXiv · 1604.01914

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

Thomas Mégarbané
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Abstract

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 about the Hasse-Weil zeta function on the moduli spaces of $17$-pointed curves of genus $3$.

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Thomas Mégarbané. 2016-04-07. 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. https://arxiv.org/abs/1604.01914

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