Abstract
In this paper, we first use classification of uni-modular lattices as a motivation to introduce semi-stable lattices. Then, as an integration over moduli spaces of semi-stable lattices, using a new arithmetic cohomology, we define a new type of non-abelian zeta functions for number fields. This is a natural generalization of what Iwasawa and Tate did for Dedekind functions. Basic facts for these zeta functions such as functional equations, singularities and residues at simple poles are discussed. Finally we introduce and study new non-abelian zeta functions for curves over finite fields, as a natural generalization of Artin’s (abelian) zeta functions, using moduli spaces of semi-stable bundles. Some interesting examples are also given here.
Graduate School of Mathematics, Nagoya University, Japan
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Weng, L. (2002). Stability and New Non-Abelian Zeta Functions. In: Kanemitsu, S., Jia, C. (eds) Number Theoretic Methods. Developments in Mathematics, vol 8. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3675-5_21
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DOI: https://doi.org/10.1007/978-1-4757-3675-5_21
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