Non-abelian zeta functions for function fields

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Abstract

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.

Original languageEnglish
Pages (from-to)973-1017
Number of pages45
JournalAmerican Journal of Mathematics
Volume127
Issue number5
DOIs
Publication statusPublished - Oct 2005

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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