Stability and New Non-Abelian Zeta Functions

  • Lin Weng
Part of the Developments in Mathematics book series (DEVM, volume 8)


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.


arithmetic cohomology adelic moduli spaces reciprocity law stability zeta functions 


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Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Lin Weng
    • 1
  1. 1.Graduate School of MathematicsKyushu UniversityFukuokaJapan

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