Zeta functions for function fields

Details Zeta functions for function fields Zeta functions for function fields

2012-02-15

arxiv.org/abs/1202.3183v2

Mathematics

Algebraic Geometry

References changed to zero my own remissness

Scientific paper

We introduce new non-abelian zeta functions for curves defined over finite fields. There are two types, i.e., pure non-abelian zetas defined using semi-stable bundles, and group zetas defined for pairs consisting of (reductive group, maximal parabolic subgroup). Basic properties such as rationality and functional equation are obtained. Moreover, conjectures on their zeros and uniformity are given. We end this paper with an explanation on why these zetas are non-abelian in nature, using our up-coming works on 'parabolic reduction, stability and the mass'. The constructions and results were announced in our paper on 'Counting Bundles' arXiv:1202.0869.

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