Abstract: Let G be a reductive group defined and split over a global function field. We are interested in the sum of multiplicities of irreducible representations containing a regular depth zero representation of G(O), where O is the ring of integral adeles, in the automorphic cuspidal spectrum. The sum is expressed in terms of the number of F_q-points of Hitchin moduli spaces of groups associated to G. When G=GL(n), it implies some cases of Deligne's conjecture by Langlands correspondence.
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ID: 818 0595 3631
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