Traces des opérateurs de Hecke sur les espaces de formes automorphes de SO₇, SO₈ ou SO₉ en niveau 1 et poids arbitraire

الأصل · EN

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 E₇, E₈ and E₈⊕ A₁, 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 Bergström, Faber and van der Geer about the Hasse-Weil zeta function on the moduli spaces of 17-pointed curves of genus 3.