• Corpus ID: 239885880

# Number of cuspidal automorphic representations and Hitchin's moduli spaces

@inproceedings{Yu2021NumberOC,
title={Number of cuspidal automorphic representations and Hitchin's moduli spaces},
author={Hongjie Yu},
year={2021}
}
Let F be the function field of a projective smooth geometrically connected curve X defined over a finite field. Let G be a split semi-simple reductive group over X. We express the sum of cuspidal multiplicities of G automorphic representations with fixed regular depth zero local behaviours as in terms of cardinality of F_q-points of Hitchin's moduli spaces of groups associated to G. We also consider the case G=GL_n where we refine the results and verify Deligne's conjecture on counting…