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Non-abelian zeta functions for function fields
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 127, Number 5, October 2005
- pp. 973-1017
- 10.1353/ajm.2005.0035
- Article
- Additional Information
In this paper we initiate a geometrically oriented construction of non-abelian zeta functions for curves defined over finite fields. More precisely, we first introduce new yet genuine non-abelian zeta functions for curves defined over finite fields, by a "weighted count" on rational points over the corresponding moduli spaces of semi-stable vector bundles using moduli interpretation of these points. Then we define non-abelian L-functions for curves over finite fields using integrations of Eisenstein series associated to L2-automorphic forms over certain generalized moduli spaces.