2004/12/01 by Lin Weng, Weng, Lin
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT
paper · pdf · doi:10.48550/arxiv.math/0412007
30 pages. to appear at Amer. J of Math
arxiv created 2004/12/01 · openalex publication_date 2004/12/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is an integrated part of our Geo-Arithmetic Program. In this paper we initiate a geometrically oriented construction of non-abelian zeta functions for curves defined over finite fields by a weighted count of semi-stable bundles. Basic properties such as rationality and functional equation are established. Examples of rank two zetas over genus two curves are given as well. Based on this and motivated by our study for non-abelian zetas of number fields, general non-abelian L functions for function fields are defined and studied using Langlands and Morris' theory of Eisenstein series.